Zhi-Wei Sun's Papers

Zhi-Wei Sun's Papers Classified by Field

A. Disjoint Residue Classes
A1. On disjoint residue classes, 　　 Discrete Math., 104(1992), no.3, 321--326. 　　 MR 93d:11005; Zbl. M. 755.11002. A2. Solutions to two problems of Huhn and Megyesi (Chinese), 　　 Chinese Ann. Math. Ser. A, 13(1992), no.6, 722--727. 　　 MR 94c:11001; Zbl. M. 770.11003.

B. Covers of the Integers by Residue Classes
B1. Some results on covering systems of congruences (Chinese, English abstract) (with Z. H. Sun), 　　 J. Southwest-China Teachers Univ., 1987, no.1, 10--15. 　　 Zbl. M. 749.11018. B2. A theorem concerning systems of residue classes, 　　 Acta Math. Univ. Comenian. (N. S.), 60(1991), no.1, 123--131. 　　 MR 92f:11007; Zbl. M. 734.11022. B3. An improvement to the Zn\'am-Newman result (Chinese, English abstract), 　　 Chinese Quart. J. Math., 6(1991), no.3, 90--96. B4. On covering systems with distinct moduli (Chinese, English abstract), 　　 J. Yangzhou Teachers College (Nat. Sci. Ed.), 11(1991), no.3, 21--27. B5. On exactly m times covers, 　　 Israel J. Math., 77(1992), no.3, 345--348. 　　 MR 93k:11007; Zbl. M. 768.11001. B6. Covering the integers by arithmetic sequences, 　　 Acta Arith., 72( 1995), no.2, 109--129. 　　 MR 96k:11013; Zbl. M. 841.11011. B7. Covering the integers by arithmetic sequences II, 　　 Trans. Amer. Math. Soc., 348(1996), no.11, 4279--4320. 　　 MR 97c:11011; Zbl. M. 884.11013. B8. Exact m-covers and the linear form $\sum^k_{s=1}x_s/n_s$, 　　 Acta Arith., 81(1997), no.2, 175--198. 　　 MR 98h:11019; Zbl. M. 871.11011. B9. Covers with less than 10 moduli and their applications (with S.-M. Yang), 　　 J. Southeast Univ. (English Edition), 14(1998), no.2, 106--114. 　　 MR 2000i:11157. Zbl. M. 1008.11003. B10.On covering multiplicity, 　　 Proc. Amer. Math. Soc., 127(1999), no.5, 1293--1300. 　　 MR 99h:11012; Zbl. M. 917.11006. B11.On n-dimensional covering systems (Chinese) (with Z. Hu), 　　 Nanjing Univ. J. Natur. Sci., 37(2001), no.4, 486--492. MR 2002j;11006; Zbl. M. 1035.11005. B12.On the function $w(x)=\|{1\le s\le k: x \equiv a_s (mod n_s)}\|$, 　　 Combinatorica, 23(2003), no.4, 681--691. MR 2004m:11013; Zbl. M. 1047.11014. B13.On m-covers and m-systems, submitted, arXiv:math.NT/0403271. B14.On the range of a covering function, 　　 J. Number Theory 111(2005), no.1, 190--196. MR 2005m:11015. B15.On odd covering systems with distinct moduli (with S. Guo), 　　 Adv. in Appl. Math. 35(2005), no.2, 182--187. B16.On covering numbers, 　　 INTEGERS: Electron. J. Combin. Number Theory 7(2007), no.2, #A33, 11pp (electronic). B17.A connection between covers of the integers and unit fractions, 　　 Adv. in Appl. Math. 38(2007), no.2, 267--274. B18.A sharp result on m-covers (with H. Pan), 　　 Proc. Amer. Math. Soc. 135(2007), no.11, 3515--3520. B19. Covers of the integers with odd moduli and their applications to the forms $x^m-2^n$ and $x^2-F_{3n}/2$ (with. K. J. Wu), 　　 Math. Comp. 78(2009), no.267, 1853--1866. B20. On m-covers and m-systems, 　　 Bull. Austral. Math. Soc. 81(2010), no.2, 223--235.

C. Covers of Groups by Cosets or Subgroups
C1. Finite coverings of groups, 　　 Fund. Math., 134(1990), no.1, 37--53. 　　 MR 91g:20031; Zbl. M. 717.20020. C2. Exact m-covers of groups by cosets, 　　 European J. Combin., 22(2001), no.3, 415--429. MR 2002a:20026; Zbl. M. 0980.20032. C3. On the Herzog-Sch\"onheim conjecture for uniform covers of groups (Abstract), 　　 J. Algebra 273(2004), no.1, 153--175. MR 2005d:20074; Zbl. M. 1067.20057. C4. Finite covers of groups by cosets or subgroups, 　　 Internat. J. Math. 17(2006), no.1, 1047--1064. C5. On covers of abelian groups by cosets (with G. Lettl), 　　 Acta Arith. 131(2008), no.4, 341-350.

D. Diophantine Equations
D1. A necessary and sufficient condition for two linear diophantine equations 　　 to have a common solution (Chinese, English abstract), 　　 Nanjing Univ. J. Natur. Sci., 25(1989), no.1, 10--17. 　　 MR 90i:11026; Zbl. M. 686.10009. D2. On integers not of the form $\pm p^a\pm q^b$, 　　 Proc. Amer. Math. Soc., 128(2000), no.4, 997--1002. 　　 MR 2000i:11157; Zbl. M. 959.11043. D3. Integers not of the form $c(2^a+2^b)+p^{\alpha}$ (with M.-H. Le), 　　 Acta Arith., 99(2001), no.2, 183--190. MR 2002e:11043; Zbl. M. 1006.11015. D4. A note on integers of the form $2^n+cp$ (with S. M. Yang), 　　 Proc. Edinburgh Math. Soc., 45(2002), no.1, 155--160. MR 2002j:11117. D5. On systems of linear diophantine equations and linear congruences 　　 (Chinese, English summary) (with H. Pan), 　　 Nanjing Univ. J. Math. Biquarterly, 19(2002), no.1, 61--67. MR 2003d:11037.

E. Covering Equivalence and Periodic Arithmetical Maps
E1. Several results on systems of residue classes, 　　 Adv. Math. (China), 18(1989), no.2, 251--252. E2. Systems of congruences with multipliers (Chinese, English abstract), 　　 Nanjing Univ. J. Math. Biquarterly, 6(1989), no.1, 124--133. 　　 MR 90m:11006; Zbl. M. 703.11002. E3. On a generalization of a conjecture of Erd\"os, 　　 Nanjing Univ. J. Natur. Sci., 27(1991), no.1, 8--15. 　　 MR 92f:11008; Zbl. M. 805.11017. E4. Algebraic approaches to periodic arithmetical maps, 　　 J. Algebra, 240(2001), no.2, 723--743. MR 2002f:11009; Zbl. M. 0974.11007. E5. On covering equivalence, 　　 in: `Analytic Number Theory' (Beijing/Kyoto, 1999), 277--302, 　　 Dev. Math., 6, Kluwer Acad. Publ., Dordrecht, 2002. MR 2003g:11014; Zbl. M. 1026.11020. E6. Arithmetic properties of periodic maps, 　　 Math. Res. Lett. 11(2004), no.2, 187--196. MR 2005g:11015. E7. A reciprocity law for uniform functions, 　　 Nanjing Univ. J. Math. Biquarterly 21(2004), no.2, 201--205. MR 2006a:11004; Zbl. M. 1066.11003. E8. Two local-global results in combinatorial number theory (Chinese), 　　 Bull. Chinese Math. Soc. 2005, no.4, 13--17. E9. A local-global theorem on periodic maps, 　　 J. Algebra 293(2005), no.2, 506--512. E10.A characterization of covering equivalence (with H. Pan), 　　 Acta Arith. 129(2007), no.4, 397--402.

F. Bernoulli Polynomials and Euler Polynomials
F1. Values of Bernoulli polynomials (with A. Granville), 　　 Pacific J. Math., 172(1996), no.1, 117--137. 　　 MR 98b:11018; Zbl. M. 856.11008. F2. General congruences for Bernoulli polynomials, 　　 Discrete Math., 262(2003), 253--276. MR 2003m:11037. 　　 [Ranked 12th among the top 25 of the most downloaded articles (from Jan. to May 2003).] F3. Some identities for Bernoulli and Euler polynomials (with K. J. Wu and H. Pan), 　　 Fibonacci Quart., 42(2004), no.4, 295-299. MR 2006a:11024; Zbl. M. 1064.11019. F4. On Euler numbers modulo powers of two, 　　 J. Number Theory 115(2005), no.2, 371--380. F5. Explicit congruences for Euler polynomials, 　　 Number Theory: Tradition and Modernization, Springer, 2006, pp. 205-218. F6. New identities involving Bernoulli and Euler polynomials (with H. Pan), 　　 J. Combin. Theory Ser. A 113(2006), no.1, 156--175. 　　 Original version: arXiv:math.NT/0407363 and arXiv:math.NT/0408223. F7. On q-Euler numbers, q-Sali\'e numbers and q-Carlitz numbers (with H. Pan), 　　 Acta Arith. 124(2006), no.1, 41--57. F8. Identities concerning Bernoulli and Euler polynomials, 　　 Acta Arith. 125(2006), no.1, 21--39. F9. Symmetric identities for Euler polynomials (with Y. Zhang and H. Pan), 　　 Graphs and Combinatorics 26(2010), no.5, 745--753. F10.On convolutions of Euler numbers, preprint.

G. Binomial Coefficients, Combinatorial Congruences, π-Series and q-Analogues
G1. A congruence for primes, 　　 Proc. Amer. Math. Soc., 123(1995), no.5, 1341--1346. 　　 MR 95f:11003; Zbl. M. 833.11001. G2. Products of binomial coefficients modulo $p^2$, 　　 Acta Arith., 97(2001), no.1, 87--98. MR 2002m:11013; Zbl. M. 986.11009. G3. A curious identity involving binomial coefficients, 　　 Integers: Electronic J. Combin. Number Theory, 2(2002), A04, 8 pp. 　　 MR 2003b:05018; Zbl. M. 0986.05012. G4. On the sum $\sum_{k\equiv r (mod m)}\binom {n}{k}$ and related congruences, 　　 Israel J. Math., 128(2002), 135--156. MR 2003d:11026. G5. Combinatorial identities in dual sequences, 　　 European J. Combin., 24(2003), no.6, 709--718. MR 2004g:05017; Zbl. M. 1024.05010. G6. A combinatorial identity with application to Catalan numbers (with H. Pan), 　　 Discrete Math. 306(2006), no.16, 1921--1940. G7. An extension of a curious binomial identity (with K. J. Wu), 　　 Int. J. Mod. Math. 2(2007), no.2, 247--251. G8. Congruences for sums of binomial coefficients (with R. Tauraso), 　　 J. Number Theory 126(2007), no.2, 287--296. 　　 [Ranked 1st among the most downloaded articles during July.-Sept. in 2007] G9. On sums of binomial coefficients and their applications, 　　 Discrete Math. 308(2008), no.18, 4231--4245. G10. Some congruences for the second order Catalan numbers (with L. L. Zhao and H. Pan), 　　 Proc. Amer. Math. Soc. 138(2010), no.1, 37--46. G11. New congruences for central binomial coefficients (with R. Tauraso), 　　 Adv. in Appl. Math. 45(2010), no.1, 125--148. G12. Binomial coefficients, Catalan numbers and Lucas quotients, 　　 Sci. China Math. 53(2010), no.9, 2473--2488. G13. Some curious congruences modulo primes (with L.-L. Zhao), 　　 J. Number Theory 130(2010), no.4, 930--935. G14. On some new congruences for binomial coefficients (with R. Tauraso), 　　 Int. J. Number Theory 7(2011), no.3, 645--662. G15. On a curious property of Bell numbers (with D. Zagier), 　　 Bull. Austral. Math. Soc. 84(2011), no.1, 153-158. (Initial arXiv version). G16. On congruences related to central binomial coefficients, 　　 J. Number Theory 131(2011), no.11, 2219-2238. G17. On Delannoy numbers and Schroder numbers, 　　 J. Number Theory 131(2011), no.12, 2387-2397. G18. Super congruences and Euler numbers, 　　 Sci. China Math. 54(2011), no.12, 2509--2535. G19. Arithmetic theory of harmonic numbers, 　　Proc. Amer. Math. Soc. 140(2012), no.2, 415--428. G20. On sums of binomial coefficients modulo p^2, 　　 Colloq. Math. 127(2012), no.1, 39-54. G21. On sums of Apery polynomials and related congruences, 　　 J. Number Theory 132(2012), no.11, 2673-2699. G22. On sums involving products of three binomial coefficients, 　　 Acta Arith. 156(2012), no.2, 123-141. G23. On divisibility of binomial coefficients, 　　 J. Austral. Math. Soc. 93(2012), no.1-2, 189-201. G24. A refinement of the Hamme-Mortenson congruence, 　　 Illinois J. Math. 56(2012), no.3, 967-979 G25. Products and sums divisible by central binomial coefficients, 　　 Electron. J. Combin. 20(2013), no.1, #P9, 1-14. [Initial version (April, 2010): arXiv:1004.4623] G26. Arithmetic theory of harmonic numbers (II) (with Li-Lu Zhao), 　　 Colloq. Math. 130(2013), no.1, 67-78. G27. Congruences for Franel numbers 　　 Adv. in Appl. Math. 51(2003), no.2, 524--535. G28. Fibonacci numbers modulo cubes of primes, 　　 Taiwan. J. Math. 17(2013), no.5, 1523-1543. G29. Supecongruences involving products of two binomial coefficients, 　　 Finite Fields Appl. 22(2013), 24--44. G30. On sums related to central binomial and trinomial coefficients, 　　in: M. B. Nathanson (ed.), Combinatorial and Additive Number Theory: CANT 2011 and 2012, 　　Springer Proc. in Math. & Stat., Vol. 101, Springer, New York, 2014, pp. 257-312. 　　[This paper contains many conjectures on congruences and 62 proposed series for 1/π. Initial version: arXiv:1101.0600] G31. Congruences involving generalized central trinomial coefficients, 　　 Sci. China Math. 57(2014), no.7, 1375-1400. arXiv:1008.3887. G32. Proof of three conjectures on congruences (with H. Pan), 　　 Sci. China Math. 57(2014), no.1, 2091-2102. G33. Some new series for 1/π and related congruences, 　　 Nanjing Univ. J. Math. Biquarterly 31(2014), no.2, 150-164. 　　[This paper contains 35 conjectural series for 1/π.] G34. Supercongruences motivated by e, 　　 J. Number Theory 147(2015), no.1, 326-341. G35. Some congruences involving binomial coefficients (with H.-Q. Cao), 　　 Colloq. Math. 139(2015), no.1, 127-136. G36. Proof of a conjectural supercongruence (with X.-Z. Meng), 　　 Finite Fields Appl. 35(2015), 86--91. G37. A new series for π³ and related congruences, 　　 Internat. J. Math. 26(2015), no.8, 1550055 (23 pages) G38. New series for some special values of L-functions, 　　Nanjing Univ. J. Math. Biquarterly 32(2015), no.2, 189-218. 　　[This paper contains 48 conjectural series for special values of L-functions and other constants.] G39. Two congruences involving harmonic numbers with applications (with G.-S. Mao), 　　 Int. J. Number Theory 12(2016), no.2, 527-539. G40. Congruences involving $g_n(x)=\sum_{k=0}^n\binom{n}{k}^2\binom{2k}{k}x^k$, 　　 Ramanujan J. 40(2016), no.3, 511-533. G41. Supercongruences involving dual sequences, 　　 Finite Fields Appl. 46(2017), 179-216. G42. Arithmetic properties of Delannoy numbers and Schr\"oder numbers, 　　 J. Number Theory 183(2018), 146-171. G43. Telescoping method and congruences for double sums (with Y.-P. Mu), 　　 Int. J. Number Theory 14(2018), no.1, 143-165. G44. Two new kinds of numbers and related divisibility results, 　　 Colloq. Math. 154(2018), no.2, 241-273. G45. Hankel-type determinants for some combinatorial sequences (with B.-X. Zhu), 　　 Int. J. Number Theory 14(2018), no.5, 1265-1277. G46. Divisibility results on Franel numbers and related polynomials (with C. Wang), 　　 Int. J. Number Theory 15 (2019), no. 2, 433--444. G47. New congruences involving products of two binomial coefficients (with G.-S. Mao), 　　 Ramanujan J. 49(2019), no. 2, 237--256. G48. Two q-analogues of Euler's formula ζ(2)=π²/6, 　　 Colloq. Math., accepted. arXiv:1802.01473 G49. On q-analogues of some series for π and π² (with Q.-H. Hou and C. Krattenthaler), 　　 Proc. Amer. Math. Soc. 147 (2019), no. 5, 1953-1961. G50. Open conjectures on congruences, 　　Nanjing Univ. J. Math. Biquarterly 36 (2019), no. 1, 1--99. G51. A new extension of the Sun-Zagier result involving Bell numbers and derangement numbers, 　　 J. Comb. Number Theory, 11 (2019), no.3, 147--152. G52. New series for powers of π and related congruences, 　　Electron. Res. Arch. 28 (2020), no. 3, 1273--1342. G53. Congruences for Apery numbers $\beta_n=\sum_{k=0}^{n}\binom{n}{k}^2\binom{n+k}{k}$ (with H.-Q. Cao and Y. Matiyasevich), 　　Int. J. Number Theory 16 (2020), no. 5, 981-1003. G54. New type series for powers of π, 　　J. Comb. Number Theory 12 (2020), no. 3, 157--208. G55. List of conjectural series for powers of π and other constants, 　　in: Ramanujan's Identities, Press of Harbin Institute of Tech., 2021, Chapter 5, pp. 205--261. 　　[This is essentially arXiv:1102.5649v47.] G56. q-Analogues of some series for powers of π (with Q.-H. Hou), 　　Ann. Comb. 25 (2021), no. 1, 167--177. G57. Supercongruences involving Lucas sequences, 　　Monatsh. Math. 196 (2021), 577--606. G58. Proof of some conjectural hypergeometric supercongruences via curious identities (with C. Wang), 　　J. Math. Anal. Appl. 505 (2022), Article ID 125575. G59. On Motzkin numbers and central trinomial coefficients, 　　Adv. in Appl. Math. 136 (2022), Article ID 102319. G60. On congruences involving Apery numbers (with W. Xia), 　　Proc. Amer. Math. Soc. 151 (2023), no. 8, 3305--3315. G61. Some new series for 1/π motivated by congruences, 　　Colloq. Math. 173 (2023), no. 1, 89--109. G62. A parametri congruence motivated by Orr's identity (with C. Wang), 　　J. Difference Equ. Appl. 29 (2023), no. 2, 198--207. G63. Some parametric congruences involving generalized central trinomial coefficients (with C. Wang), 　　Rev. R. Acad. Cienc. Exactas Fis. Nat. Ser. A Mat. RACSAM 118 (2024), Article 3. G64. New congruences involving harmonic numbers, 　　Nanjing Univ. J. Math. Biquarterly, 40 (2023), no. 1, 1--33. G65. Series with summands involving harmonic numbers, 　　in: M. Nathanson (ed.), Combinatorial and Additive Number Theory VI, 　　Springer Proc. Math. Stat., Springer, 2024, in press. G66. Various congruences involving binomial coefficients and higher-order Catalan numbers , 　　 preprint, arXiv:0909.3808. G67. Congruences involving binomial coefficients and Lucas sequences, 　　 preprint, arXiv:0912.1280. G68. Curious congruences for Fibonacci numbers, 　　 preprint, arXiv:0912.2671.

H. Primes, Practical Numbers, and p-adic Methods and Applications
H1. Polynomial extension of Fleck's congruence, 　　 Acta Arith. 122(2006), no.1, 91--100. H2. A number-theoretic approach to homotopy exponents of SU(n) (with D. M. Davis), 　　 J. Pure Appl. Algebra 209(2007), no.1, 57--69. H3. Combinatorial congruences modulo prime powers (with D. M. Davis), 　　 Trans. Amer. Math. Soc. 359(2007), no.11, 5525--5553. H4. Combinatorial congruences and Stirling numbers, 　　 Acta Arith. 126(2007), no.4, 387--398. H5. On Fleck quotients (with D. Wan), 　　 Acta Arith. 127(2007), no.4, 337--363. H6. Lucas-type congruences for cyclotomic $\psi$-coefficients (with D. Wan), 　　 Int. J. Number Theory 4(2008), no. 2, 155--170. H7. On 2-adic orders of some binomial sums (with H. Pan), 　　 J. Number Theory 130(2010), no.12, 2701--2706. H8. p-adic valuations of some sums of multinomial coefficients, 　　 Acta Arith. 148(2011), no.1, 63-76. H9. Binomial coefficients and the ring of p-adic integers (with W. Zhang), 　　 Proc. Amer. Math. Soc. 139(2011), no.5, 1569--1577. H10.Extensions of Wilson's lemma and the Ax-Katz theorem, 　　 preprint, arXiv:math.NT/0608560. H11.Fleck quotients and Bernoulli numbers, 　　 submitted, arXiv:math.NT/0608328. H12.Some q-congruences related to 3-adic valuations (with H. Pan), 　　 Adv. in Appl. Math. 49(2012), no.3-5, 263-270. H13.On a sequence involving sums of primes, 　　 Bull. Aust. Math. Soc. 88(2003), no.2, 197-205. H14.Conjectures involving arithmetical sequences, 　　 in: Number Theory: Arithmetic in Shangri-La (eds., S. Kanemitsu, H. Li and J. Liu), Proc. 6th China-Japan Seminar 　　 (Shanghai, August 15-17, 2011), World Sci., Singapore, 2013, pp. 244-258. H15.On functions taking only prime values, 　　 J. Number Theory 133(2013), no.8, 2794-2812. H16.p-adic congruences motivated by series, 　　 J. Number Theory 134(2014), no.1, 181-196. H17. Problems on combinatorial properties of primes, 　　 in: M. Kaneko, S. Kanemitsu and J. Liu (eds.), Number Theory: Plowing and Starring through High Wave Forms, Proc. 7th China-Japan Seminar 　　 (Fukuoka, Oct. 28--Nov. 1, 2013), Ser. Number Theory Appl., Vol. 11, World Sci., Singapore, 2015, pp. 169-187. 　　 [This paper contains 60 challenging conjectures whose solutions might be beyond the intelligence of human beings.] H18.The least modulus for which consecutive polynomial values are distinct, 　　J. Number Theory 160 (2016), 108-116. H19. On a pair of zeta functions, 　　Int. J. Number Theory 12(2016), no.8, 2323-2342. 　　[This paper contains a hypothesis which implies the Riemann Hypothesis.] H20. A new theorem on the prime-counting function, 　　Ramanujan J. 42(2017), no.1, 59-67. H21. Conjectures on representations involving primes, 　　in: M. Nathanson (ed.), Combinatorial and Additive Number Theory II, 　　Springer Proc. Math. Stat., Vol. 220, Springer, New York, Cham, 2017, pp. 279-310. 　　[This paper contains 100 conjectures on representations involving primes or related things.] H22. New conjectures on representations of integers (I), 　　Nanjing Univ. J. Math. Biquarterly 34(2017), no.2, 97-120. H23. Consecutive primes and Legendre symbols (with H. Pan), 　　Acta Arith. 190 (2019), no. 3, 209--220. H24. New observations on primitive roots modulo primes, 　　Nanjing Univ. J. Math. Biquarterly 36 (2019), no. 2, 108--133. H25. On the set {π(kn): k=1,2,3,...} （with L. Zhao）, 　　J. Comb. Number Theory 11 (2019), no. 2, 97--102. H26. On practical numbers of some special forms (with L.-Y. Wang), 　　Houston J. Math. 48 (2022), no. 2, 241--247.

I. Restricted Sumsets and Zero-sum Problems
I1. On sums of distinct representatives (with H.-Q. Cao), 　　 Acta Arith., 87(1998), no.2, 159--169. 　　 MR 99k:11021; Zbl. M. 920.11010. I2. A note on the Erd\"os-Ginzburg-Ziv theorem (with J.-X. Liu), 　　 Nanjing Univ. J. Natur. Sci., 37(2001), no.4, 473--476. MR 2002j:11014. I3. Restricted sums of subsets of $\Bbb Z$, 　　 Acta Arith., 99(2001), no.1, 41--60. MR 2002j:11016; Zbl. M. 0974.11009. I4. Hall's theorem revisited, 　　 Proc. Amer. Math. Soc., 129(2001), no.10, 3129--3131. MR 2002h:05007; Zbl. M. 0966.05067. I5. Restricted sums in a field (with Q. H. Hou), 　　 Acta Arith., 102(2002), no.3, 239--249. MR 2003e:11025; Zbl. M. 0988.11008. I6. Sums of subsets with polynomial restrictions (with J. X. Liu), 　　 J. Number Theory, 97(2002), no.2, 301--304. MR 2004c:11027; Zbl. M. 1034.11021. I7. A lower bound for $\|{a+b: a\in A, b\in B, P(a,b)\not=0}\|$ (with H. Pan), 　　 J. Combin. Theory Ser. A, 100(2002), no.2, 387--393. MR 2003k:11016; Zbl. M. 1020.11080. I8. Unification of zero-sum problems, subset sums and covers of Z (Research Announcement), 　　 Electron. Res. Announc. Amer. Math. Soc., 9(2003), 51--60. MR 2004i:11017; Zbl. M. 1062.11015. 　　 [Submitted on 2003-03-20 and communicated by R. L. Graham.] I9. On Snevily's conjecture and restricted sumsets, 　　 J. Combin. Theory Ser. A, 103(2003), no.2, 291--304. MR 2004k:11026; Zbl. M. 1042.11016. I10.On various restricted sumsets (with Y. N. Yeh), 　　 J. Number Theory 114(2005), no.2, 209--220, I11.Restricted sumsets and a conjecture of Lev (with H. Pan), 　　 Israel J. Math. 154(2006), no.1, 21--28. I12.On the number of zero-sum subsequences (with H.-Q. Cao), 　　 Discrete Math. 307(2007), no.13, 1687--1691. I13. A survey of problems and results on restricted sumsets, 　　 in: Number Theory (edited by S. Kanemitsu and J.-Y. Liu), World Sci., Singapore, 2007, 190--213. I14.On value sets of polynomials over a field, 　　 Finite Fields Appl. 14(2008), no.2, 470-481. I15.An additive theorem and restricted sumsets, 　　 Math. Res. Lett. 15(2008), no.6, 1263-1276. I16.A variant of Tao's method with application to restricted sumsets (with S. Guo), 　　 J. Number Theory 129(2009), no.2, 434-438. I17.Zero-sum problems for abelian p-groups and covers of the integers by residue classes, 　　 Israel J. Math. 170(2009), 235-252. I18.On Bialostocki's conjecture for zero-sum sequences (with S. Guo), 　　 Acta Arith., 140(2009), no.4, 329--334. I19.A new extension of the Erdos-Heilbronn conjecture (with H. Pan), 　　 J. Combin. Theory Ser. A 116(2009), no.8, 1374--1381. I20.Exterior algebras and two conjectures on finite abelian groups (with T. Feng and Q. Xiang), 　　 Israel J. Math. 182(2011), no.1, 425--437. I21.Linear extension of the Erdos-Heilbronn conjecture (with Lilu Zhao), 　　 J. Combin. Theory Ser. A 119(2012), 364--381. I22.On weighted zero-sum sequences (with S. D. Adhikari and D. J. Grynkiewicz), 　　 Adv. in Appl. Math. 48(2012), no.3, 506--527. I23. On a sumset problem for integers (with. S.-S. Du and H.-Q. Cao), 　　Electron. J. Combin., 21(2014), no.1, #P1.13, 1--25. I24. On a permutation problem for finite abelian groups (with. F. Ge), 　　Electron. J. Combin., 24(2017), no.1, #P1.17, 1--6. I25. Some new problems in additive combinatorics, 　　Nanjing Univ. J. Math. Biquarterly 36 (2019), no. 2, 134--155. I26. On permutations of {1,...,n} and related topics, 　　J. Algebraic Combin. 54 (2021), 893--912. I27. On sums and products in a field (with G.-L. Zhou), 　　Czechoslovak Math. J. 72 (2022), 817--823.

J. Dedekind Sums and Related Sums
J1. Sums of minima and maxima, 　　 Discrete Math., 257(2002), no.1, 143--159. 　　 MR 2003g:11037; Zbl. M. 1007.05018 J2. Generalizations of Knopp's identity (with B. F. Chen), 　　 J. Number Theory, 97(2002), no.1, 186--198. 　　 MR 2003i:11054; Zbl. M. 1033.11017.

K. Linear Recurrences and Combinatorial Sequences
K1. Fibonacci numbers and Fermat's last theorem (with Z. H. Sun), 　　 Acta Arith., 60(1992), no.4, 371--388. 　　 MR 93e:11025; Zbl. M. 725.11009, 739.11004. K2. Some identities on linear recurrent sequences of second order 　　 (Chinese, English abstract) (with H. Hu), 　　 Nanjing Univ. J. Math. Biquarterly, 17(2000), no.1, 86--92. 　　 MR 2001e:11012; Zbl. M. 1020.11013. K3. Reciprocal sums of second-order recurrent sequences (with H. Hu and J.-X. Liu), 　　 Fibonacci Quart., 39(2001), no.3, 214--220. MR 2002d:11016; Zbl. M. 0992.11014. K4. An extension of Lucas' theorem (with H. Hu), 　　 Proc. Amer. Math. Soc., 129(2001), no.12, 3471--3478. MR 2002i:11019. K5. On harmonic numbers and Lucas sequences, 　　 Math. Publ. Debrecen 80(2012), no. 1-2, 25--41. K6. On monotonicity of some combinatorial sequences (with Q.-H. Hou and H. Wen), 　　 Math. Publ. Debrecen 85(2014), no.3-4, 285-295.

L. Quadratic Forms, Quadratic Fields, Power Residues, and Representations of Integers
L1. Binomial coefficients and quadratic fields, 　　 Proc. Amer. Math. Soc. 134(2006), no.8, 2213--2222. L2. Simple arguments on consecutive power residues, 　　 J. Number Theory 124(2007), no.1, 57--61. L3. Mixed sums of squares and triangular numbers, 　　 Acta Arith. 127(2007), no.2, 103--113. L4. Mixed sums of squares and triangular numbers (II) (with S. Guo and H. Pan), 　　 Integers: Electron. J. Combin. Theory, 7(2007), #A56, 5 pp.(electronic) L5. On sums of primes and triangular numbers, 　　 Journal of Combinatorics and Number Theory 1(2009), no.1, 65--76. arXiv:0803.3737. L6. Mixed sums of squares and triangular number (III) (with B. K. Oh), 　　 J. Number Theory 129(2009), no.4, 964-969. L7. Mixed sums of primes and other terms, 　　 in: Additive Number Theory (edited by D. Chudnovsky and G. Chudnovsky), pp. 341-353, Springer, New York, 2010. L8. On almost universal mixed sums of squares and triangular numbers (with B. Kane), 　　 Trans. Amer. Math. Soc. 362(2010), no.12, 6425--6455. L9. Conjectures and results on x² mod p² with 4p=x² + dy², 　　 in: Number Theory and Related Area (eds., Y. Ouyang, C. Xing, F. Xu and P. Zhang), 　　 Adv. Lect. Math. 27, Higher Education Press and International Press, Beijing-Boston, 2013, pp.149-197. arXiv:1103.4325. L10.Connections between p=x² + 3y² and Franel numbers, 　　J. Number Theory 133(2013), no.9, 2914-2928. L11.On sums related to central binomial and trinomial coefficients, 　　in: M. B. Nathanson (ed.), Combinatorial and Additive Number Theory: CANT 2011 and 2012, 　　Springer Proc. in Math. & Stat., Vol. 101, Springer, New York, 2014, pp. 257-312. 　　[This paper contains many conjectures on congruences and 62 proposed series for 1/π. Initial version: arXiv:1101.0600] L12.On universal sums of polygonal numbers, 　　Sci. China Math. 58(2015), no.7, 1367--1396. L13.On some universal sums of generalized polygonal numbers (with F. Ge), 　　Colloq. Math. 145(2016), no.1, 149-155. L14. A result similar to Lagrange's theorem, 　　J. Number Theory 162(2016), 190-211. L15. On x(ax+1)+y(by+1)+z(cz+1) and x(ax+b)+y(ay+c)+z(az+d), 　　J. Number Theory 171(2017), 275-283. L16. Refining Lagrange's four-square theorem, 　　J. Number Theory 175(2017), 167-190. 　　[This paper contains my challenging 1-3-5-Conjecture.] L17. Sums of four polygonal numbers with coefficients (with X.-Z. Meng), 　　Acta Arith. 180(2017), no.3, 229-249. arXiv:1608.02022 L18. Some variants of Lagrange's four squares theorem (with Y.-C. Sun), 　　Acta Arith. 183(2018), no.4, 339-356. L19. On universal sums x(ax+b)/2+y(cy+d)/2+z(ez+f)/2, 　　Nanjing Univ. J. Math. Biquarterly 35(2018), no.2, 85-199. L20.. Some universal quadratic sums over the integers (with H.-L. Wu), 　　Electron. Res. Arch., 27 (2019), 69-87. L21. On some determinants with Legendre symbol entries, 　　Finite Fields Appl. 56 (2019), 285-307. L22. Restricted sums of four squares, 　　Int. J. Number Theory 15 (2019), no. 9, 1863--1893. L23. Quadratic residues and related permutations and identities, 　　Finite Fields Appl. 59 (2019), 246-283. L24. Universal sums of three quadratic polynomials, 　　Sci. China Math. 63 (2020), no. 3, 501-520. L25. On the 1-3-5 conjecture and related topics (with H.-L. Wu), 　　Acta Arith. 193 (2020), no. 3, 253--268. L26. On some determinants involving Jacobi symbols (with D. Krachun, F. Petrov and M. Vsemirnov), 　　Finite Fields Appl. 64 (2020), Article 101672. L27. On sums of four pentagonal numbers with coefficients (with D. Krachun), 　　Electron. Res. Arch. 28 (2020), no. 1, 559-566. L28. Proof of some conjectures involving quadratic residues (with F. Petrov), 　　Electron. Res. Arch. 28 (2020), no. 2, 589-597. L29. Quadratic residues and quartic residues modulo primes, 　　Int. J. Number Theory 16 (2020), no. 8, 1833--1858. L30. Each positive rational number has the form $\varphi(m^2)/\varphi(n^2)$ (with D. Krachun), 　　Amer. Math. Monthly 127 (2020), no. 9, 847--849. L31. Proof of three conjectures on determinants related to quadratic residues (with D. Grinberg and L. Zhao), 　　Linear Multilinear Algebra 70 (2022), no. 19, 3734--3746. L32. A new theorem on quadratic residues modulo primes (with Q.-H. Hou and H. Pan), 　　C. R. Math. Acad. Sci. Paris 360 (2022), 1065-1069. L33. Trigonometric identities and quadratic residues, 　　Publ. Math. Debrecen 102 (2023), no. 1-2, 111--138. L34. The tangent function and power residues modulo primes, 　　Czechoslovak Math. J. , in press. arXiv:2208.05928 L35. Representing n as n=x+y+z with x²+y²+z² a square (with C. Huang), 　　Arch. Math. (Basel), 121 (2023), no. 3, 231--239. L36. Arithmetic progressions represented by diagonal ternary quadratic forms (with H.-L. Wu), 　　Nanjing Univ. J. Math. Biquarterly, 40 (2023), no. 1, 54--71.

M. Hilbert's Tenth Problem and Diophantine Representations
M1. Some diophantine representations related to $\binom{PX}{QX}$ (Chinese, English abstract), 　　 in: Selected Papers on BCI and BCK Algebras and Computer Logics (edited by B.-Y. Shen), 　　 Shanghai Jiaotong Univ. Press, Shanghai, 1991, 131--138. M2. Reduction of unknowns in Diophantine representations, 　　 Sci. China Ser. A, 35(1992), no.3, 257--269. 　　 Chinese Edition, 1991, no.10, 1030--1040. 　　 MR 93h:11039; Zbl. M. 773.11077. M3. Singlefold Diophantine representation of the sequence 　　 $u_0=0, u_1=1$ and $u_{n+2}=mu_{n+1}+u_n$, 　　 in: Pure and Applied Logic (edited by J.-W. Zhang), 　　 Beijing Univ. Press, Beijing, 1992, 97--101. M4. A new relation-combining theorem and its application, 　　 Z. Math. Logik Grundlag. Math., 38(1992), no.3, 209--212. 　　 MR 94m:03069; Zbl. M. 793.03004. M5. Jone's work on Hilbert's tenth problem and related topics (Chinese, English abstract), 　　 Adv. Math. (China), 22(1993), no.4, 312--331. 　　 MR 94j:03089; Zbl. M. 791.03005. M6. Further results on Hilbert's Tenth Problem, 　　Sci. China Math., 64 (2021), no. 2, 281--306. M7. Q\Z is diophantine over Q with 32 unknowns (with G.-R. Zhang), 　　Bull. Pol. Acad. Sci. Math. 70 (2022), no. 2, 93--106. M8. On Diophantine equations over Z[i] with 52 unknowns (with Yu. Matiyasevich), 　　Proc. of the 2019 Asian Logic Conf., World Sci. Press, Singapore, to appear. arXiv:2002.12136

N. Combinatorics, Determinants and Permanents
N1. On the unique representability of spikes over prime fields (with Z. Y. Wu), 　　 Discrete Math. 306(2006), no.15, 1798--1804. N2. Determination of the two-color Rado number for a_1x_1+...+a_mx_m=x_0 (with S. Guo), 　　 J. Combin. Theory Ser. A, 115(2008), no.2, 345--353. N3. Groups in combinatorial number theory, 　　 in: Proceedings of the 4th International Congress of Chinese Mathematicians (Hangzhou, 2007), 　　 Vol. I, Higher Education Press, Beijing, 2007, pp. 475--495. N4. Permutations of {1,...,n} and related topics, 　　J. Algebraic Combin. 54 (2021), 893--912. N5. Proof of a conjecture involving derangements and roots of unity (with H. Wang), 　　Electron. J. Combin., 30 (2023), no. 2, #P2.1, 10 pages. N6. On some determinants and permanents, 　　Acta Math. Sinica Chin. Ser. 67 (2024), no. 2, 286--295. [For the English version, see arXiv:2207.13039] N7. Legendre symbols related to certain determinants (with X.-Q. Luo), 　　Bull. Malays. Math. Sci. Soc., 46 (2023), no. 4, Article No. 119, 20 pages. N8. A new trigonometric identity with applications (with H. Pan), 　　Contrib. Discrete Math., in press. N9. On some determinants involving the tangent function, 　　Ramanujan J., in press. arXiv:1901.04837 N10.On certain determinants and related Legendre symbols (with H. Wang), 　　Bull. Malays. Math. Sci. Soc., 47 (2024), no. 2, Article No. 58, 19 pages.

O. Logic and Computer Science
O1. Some results on recursive functions (Chinese, English abstract), 　　 Nanjing Univ. J. Math. Biquarterly, 4(1987), no.2, 196--206. 　　 Zbl. M. 657.03022. O2. Definition of degree of unsolvablity on real numbers (with X. Z. Zheng and D. C. Ding), 　　 Chinese Sci. Bull. (Chinese Edition), 38(1993), no.3, 203--206. O3. Equivalent propositions about $R$-reconstructions in open logic (with K. L. Su), 　　 Nanjing Univ. J. Math. Biquarterly, 11(1994), no.1, 6--9. 　　 MR 95k:68219; Zbl. M. 808.03012. O4. Fixed points of a class of operators in open logic (with K. L. Su, D. C. Ding and L. Qian), 　　 Acta Sci. Natur. Univ. Norm. Hunan., 17(1994), no.3, 21--23. 　　 MR 96c:68189; Zbl. M. 816.03014. O5. Class of models for a rejection by reasonal facts (with K. L. Su, D. C. Ding and L. Qian), 　　 Chinese J. Comput., 17(1994), no.5, 361--366. O6. Reconstructions and epistemic processes in the open logic system 　　 (with K. L. Su, D. C. Ding and L. Qian), 　　 in: Proc. of the National Confer. on the Fundamental Theories of Artificial Intelligence, 　　 Tsinghua Univ. Press, Beijing, 1994, pp. 163--168. O7. The continuum Hypothesis and Turing degrees (with K. L. Su and D. C. Ding), 　　 Acta Math. Sinica, 39(1996), no.1, 71--75. 　　 MR 97e:03064; Zbl. M. 863.03023. O8. On the emptiness problem for two-way NFA with one reversal-bounded counter 　　 (with Z. Dang and O. H. Ibarra), 　　 in: P. Bose and P. Morin (Eds.), Algorithms and Computation, 　　 Lecture Notes in Computer Science, Vol. 2518, Springer, 2002, pp. 103--114. O9. Safety verification for two-way finite automata with monotonic counters 　　 (with O. H. Ibarra and Z. Dang), 　　 in: M. Ito and M. Toyama (Eds.), Developments in Language Theory 2002, 　　 Lecture Notes in Computer Science, Vol. 2450, Springer, 2003, pp. 326--338. Zbl. M. 1015.68112. O10.On two-way nondeterministic finite automata with 　　 one reversal-bounded counter (with Z. Dang and O. Ibarra), 　　 Theoret. Comput. Sci. 330(2005), no.1, 59--79. MR 2005h:68068.


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