241. On certain determinants and related Legendre symbols (with H. Wang),
Bull. Malays. Math. Sci. Soc., 47 (2024), no. 2, Article No. 58, 19 pages.
240. On some determinants involving the tangent function,
Ramanujan J., in press. arXiv:1901.04837
239. A new trigonometric identity with applications (with H. Pan),
Contrib. Discrete Math., in press.
238. On Diophantine equations over Z[i] with 52 unknowns (with Y. Matiyasevich),
Proc. of the 2019 Asian Logic Conf., World Sci. Press, Singapore, to appear. arXiv:2002.12136
237. Series with summands involving harmonic numbers,
in: M. Nathanson (ed.), Combinatorial and Additive Number Theory VI,
Springer Proc. Math. Stat., Springer, 2024, in press.
236. On some determinants and permanents,
Acta Math. Sinica Chin. Ser. 67 (2024), no. 2, 286--295. For the English version of this paper, see arXiv:2207.13039
235. 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.
234. Fibonacci Numbers and Hilbet's Tenth Problem (《Fibonacci数与Hilbert第十问题》) (in Chinese),
Harbin Institute of Technology Press (哈尔滨工业大学出版社), 2024.
233. Arithmetic progressions represented by diagonal ternary quadratic forms (with H.-L. Wu),
Nanjing Univ. J. Math. Biquarterly, 40 (2023), no. 1, 54--71.
232. 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.
231. Legendre symbols related to certain determinants (with X.-Q. Luo),
Bull. Malays. Math. Sci. Soc., 46 (2023), no. 4, Article No. 119, 20 pages.
230. Proof of a conjecture involving derangements and roots of unity (with H. Wang),
Electron. J. Combin., 30 (2023), no. 2, #P2.1, 10 pages.
229. A parametri congruence motivated by Orr's identity (with C. Wang),
J. Difference Equ. Appl. 29 (2023), no. 2, 198--207.
228. Some new series for 1/π motivated by congruences,
Colloq. Math. 173 (2023), no. 1, 89--109.
227. On congruences involving Apery numbers (with W. Xia),
Proc. Amer. Math. Soc. 151 (2023), no. 8, 3305--3315.
226. The tangent function and power residues modulo primes,
Czechoslovak Math. J. 73 (2023), no. 3, 971--978.
225. Trigonometric identities and quadratic residues,
Publ. Math. Debrecen 102 (2023), no. 1-2, 111--138.
224. New congruences involving harmonic numbers,
Nanjing Univ. J. Math. Biquarterly, 40 (2023), no. 1, 1--33.
223. Q\Z is diophantine over Q with 32 unknowns (with G.-R. Zhang),
Bull. Pol. Acad. Sci. Math. 70 (2022), no. 2, 93--106.
222. On practical numbers of some special forms (with L.-Y. Wang),
Houston J. Math. 48 (2022), no. 2, 241--247.
221. 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.
220. On Motzkin numbers and central trinomial coefficients,
Adv. in Appl. Math.
136 (2022), Article ID 102319.
219. Modern Algebra (近世代数),
Nanjing University Press (南京大学出版社), 2022. [This is a textbook.]
218. Proof of some conjectural hypergeometric supercongruences via curious identities (with C. Wang),
J. Math. Anal. Appl. 505 (2022), Article ID 125575.
217. 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.
216. On sums and products in a field (with G.-L. Zhou),
Czechoslovak Math. J. 72 (2022), 817--823.
215. Supercongruences involving Lucas sequences,
Monatsh. Math. 196 (2021), 577--606.
214. On permutations of {1,...,n} and related topics,
J. Algebraic Combin. 54 (2021), 893--912.
213. q-Analogues of some series for powers of π (with Q.-H. Hou),
Ann. Comb. 25 (2021), no. 1, 167--177.
212. New Conjectures in Number Theory and Combinatorics (《数论与组合中的新猜想》),
Harbin Institute of Technology Press (哈尔滨工业大学出版社), 2021.
[This book contains 820 open conjectures posed by the author.]
211. 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.]
210. Further results on Hilbert's Tenth Problem,
Sci. China Math., 64 (2021), no. 2, 281--306.
209. New type series for powers of π,
J. Comb. Number Theory 12 (2020), no. 3, 157--208.
208. 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.
207. New series for powers of π and related congruences,
Electron. Res. Arch. 28 (2020), no. 3, 1273--1342.
206. 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.
205. Quadratic residues and quartic residues modulo primes,
Int. J. Number Theory 16 (2020), no. 8, 1833--1858.
204. Proof of some conjectures involving quadratic residues (with F. Petrov),
Electron. Res. Arch. 28 (2020), no. 2, 589-597.
203. On sums of four pentagonal numbers with coefficients (with D. Krachun),
Electron. Res. Arch. 28 (2020), no. 1, 559-566.
202. On some determinants involving Jacobi symbols (with D. Krachun, F. Petrov and M. Vsemirnov),
Finite Fields Appl. 64 (2020), Article 101672.
201. On the 1-3-5 conjecture and related topics (with H.-L. Wu),
Acta Arith. 193 (2020), no. 3, 253--268.
200. Universal sums of three quadratic polynomials,
Sci. China Math. 63 (2020), no. 3, 501-520.
199. A new extension of the Sun-Zagier result involving Bell numbers
and derangement numbers,
J. Comb. Number Theory,
11 (2019), no.3, 147--152.
198. On the set {π(kn): k=1,2,3,...} (with L. Zhao),
J. Comb. Number Theory 11 (2019), no. 2, 97--102.
197. Some universal quadratic sums over the integers (with H.-L. Wu),
Electron. Res. Arch. 27 (2019), 69-87.
196. Some new problems in additive combinatorics,
Nanjing Univ. J. Math. Biquarterly 36 (2019), no. 2, 134-155.
195. New observations on primitive roots modulo primes,
Nanjing Univ. J. Math. Biquarterly 36 (2019), no. 2, 108-133.
194. Quadratic residues and related permutations and identities,
Finite Fields Appl. 59 (2019), 246-283.
193. Restricted sums of four squares,
Int. J. Number Theory 15 (2019), no. 9, 1863-1893.
192. On some determinants with Legendre symbol entries,
Finite Fields Appl. 56(2019), 285--307.
191. Open conjectures on congruences,
Nanjing Univ. J. Math. Biquarterly 36 (2019), no. 1, 1-99.
[This paper contains 100 unsolved conjectures on congruences posed by the author.]
190. Consecutive primes and Legendre symbols (with H. Pan),
Acta Arith. 190 (2019), no. 3, 209--220.
189. 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.
188. Two q-analogues of Euler's formula ζ(2)=π2/6,
Colloq. Math. 158 (2019), no. 2, 313--320.
187. New congruences involving products of two binomial coefficients (with G.-S. Mao),
Ramanujan J. 49(2019), no. 2, 237--256.
186. Divisibility results on Franel numbers and related polynomials (with C. Wang),
Int. J. Number Theory 15 (2019), no. 2, 433--444.
185. 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.
184. Sone variants of Lagrange's four squares theorem (with Y.-C. Sun),
Acta Arith. 183(2018), no.4, 339-356.
183. Hankel-type determinants for some combinatorial sequences (with B.-X. Zhu),
Int. J. Number Theory 14(2018), no.5, 1265-1277.
182. Two new kinds of numbers and related divisibility results,
Colloq. Math. 154(2018), no.2, 241-273.
181. Telescoping method and congruences for
double sums (with Y.-P. Mu),
Int. J. Number Theory 14(2018), no.1, 143-165.
180. Arithmetic properties of Delannoy numbers and Schr\"oder numbers,
J. Number Theory 183(2018), 146-171.
179. New conjectures on representations of integers (I),
Nanjing Univ. J. Math. Biquarterly 34(2017), no.2, 97-120.
178. Sums of four polygonal numbers with coefficients (with X.-Z. Meng),
Acta Arith. 180(2017), no.3, 229-249.
177. Supercongruences involving dual sequences,
Finite Fields Appl. 46(2017), 179-216.
176. Conjectures on representations involving primes,
in: M. Nathanson (ed.), Combinatorial and Additive Number Theory II,
Springer Proc. Math. Stat., Vol. 220, Springer, Cham, 2017, pp. 279-310.
[This paper contains 100 conjectures on representations involving primes or related things.]
175. On a permutation problem for finite abelian groups (with. F. Ge),
Electron. J. Combin. 24(2017), no.1, #P1.17, 1-6.
174. Refining Lagrange's four-square theorem,
J. Number Theory 175(2017), 167-190.
[This paper contains my challenging 1-3-5-Conjecture.]
173. 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.
172. A new theorem on the prime-counting function,
Ramanujan J. 42(2017), no.1, 59-67.
171. On a pair of zeta functions,
Int. J. Number Theory 12(2016), no.8, 2323-2342.
[This paper contains a simple hypothesis which implies the Riemann Hypothesis.]
170. A result similar to Lagrange's theorem,
J. Number Theory 162(2016), 190-211.
169. Two congruences involving harmonic numbers with applications (with G.-S. Mao),
Int. J. Number Theory 12(2016), no.2, 527-539.
168. The least modulus for which consecutive polynomial values are distinct,
J. Number Theory 160 (2016), 108-116.
167. 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.
166. On some universal sums of generalized polygonal numbers (with F. Ge),
Colloq. Math. 145(2016), no.1, 149-155.
165. 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.]
164. A new series for π^3 and related congruences,
Internat. J. Math. 26 (2015), no.8, 1550055 (23 pages).
163. Proof of a conjectural supercongruence (with X.-Z. Meng),
Finite Fields Appl. 35 (2015), 86-91.
162. Some congruences involving binomial coefficients (with H.-Q. Cao),
Colloq. Math. 139 (2015), no.1, 127-136.
161. On universal sums of polygonal numbers,
Sci. China Math. 58 (2015), no.7, 1367-1396.
160. 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.]
159. Supercongruences motivated by e,
J. Number Theory 147(2015), no.1, 326-341.
158. On monotonicity of some combinatorial sequences (with Q.-H. Hou and H. Wen),
Publ. Math. Debrecen 85(2014), no.3-4, 285-295.
157. 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.]
156. Introduction to Basic Number Theory (《基础数论入门》), Press of Harbin Institute of Technology (哈尔滨工业大学出版社), 2014.
155. Proof of three conjectures on congruences (with H. Pan),
Sci. China Math. 57(2014), no.10, 2091-2102.
154. Congruences involving generalized central trinomial coefficients,
Sci. China Math. 57(2014), no.7, 1375-1400.
153. p-adic congruences motivated by series,
J. Number Theory 134(2014), no.1, 181-196.
152. 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.
151. 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]
150. Connections between p=x2+3y2
and Franel numbers,
J. Number Theory 133(2013), no.9, 2914-2928.
149. On functions taking only prime values,
J. Number Theory 133(2013), no.8, 2794-2812.
[This published paper contains many mysterious conjectures on primes.]
148. Supercongruences involving products of two binomial coefficients,
Finite Fields Appl. 22(2013), 24-44.
147. Fibonacci numbers modulo cubes of primes,
Taiwanese J. Math. 17(2013), no.5, 1523-1543.
146. Congruences for Franel numbers,
Adv. in Appl. Math. 51(2013), no.4, 524-535.
145. Arithmetic theory of harmonic numbers (II) (with Li-Lu Zhao),
Colloq. Math. 130(2013), no.1, 67--78.
144. 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]
143. 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.
142. On a sequence involving sums of primes,
Bull. Aust. Math. Soc. 88(2013), no.2, 197-205.
141. 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.
140. A refinement of a congruence result by van Hamme and Mortenson,
Illinois J. Math. 56(2012), no.3, 967--979.
139. On divisibility of binomial coefficients,
J. Austral. Math. Soc. 93(2012), no.1-2, 189-201.
138. On sums involving products of three binomial coefficients,
Acta Arith. 156(2012), no.2, 123-141.
137. On sums of Apery polynomials and related congruences,
J. Number Theory 132(2012), no.11, 2673-2699.
136. Some q-congruences related to 3-adic valuations (with H. Pan),
Adv. in Appl. Math. 49(2012), no.3-5, 263-270.
135. On sums of binomial coefficients modulo
p2,
Colloq. Math. 127(2012), no.1, 39-54.
134. On weighted zero-sum sequences (with S. D. Adhikari and D. J. Grynkiewicz),
Adv. in Appl. Math. 48(2012), no.3, 506-527.
133. Linear exntension of the Erdos-Heilbronn conjecture
(with Lilu Zhao),
J.
Combin. Theory Ser. A 119(2012), no.2, 364-381.
132. On harmonic numbers and Lucas sequences,
Publ. Math. Debrecen 80(2012), no.1-2, 25--41.
131. Arithmetic theory of harmonic numbers,
Proc. Amer. Math. Soc. 140(2012), no.2, 415--428.
130. Super congruences and Euler numbers,
Sci. China Math. 54(2011), no.12, 2509--2535.
129. Binomial coefficients and the ring of p-adic integers
(with W. Zhang),
Proc. Amer. Math. Soc. 139(2011), no.5, 1569--1577.
128. On Delannoy numbers and Schroder numbers,
J. Number Theory
131(2011), no.12, 2387-2397.
127. On congruences related to central binomial coefficients,
J. Number Theory 131(2011),
no.11, 2219-2238.
126. p-adic valuations of some sums of multinomial coefficients,
Acta Arith.
148(2011), no.1, 63-76.
125. On a curious property of Bell numbers
(with D. Zagier),
Bull. Aust. Math. Soc.
84(2011), no.1, 153-158.
((Initial arXiv version).
124. Exterior algebras and two conjectures on finite abelian groups (with T. Feng and
Q. Xiang),
Israel J. Math. 182(2011), no.1, 425--437.
123. On some new congruences for binomial coefficients (with R. Tauraso),
Int. J. Number Theory 7(2011), no.3, 645--662.
122. On almost universal mixed sums of squares and triangular numbers
(with B. Kane),
Trans. Amer. Math. Soc. 362(2010), no.12, 6425--6455.
121. On 2-adic orders of some binomial sums (with H. Pan),
J. Number Theory 130(2010), no.12, 2701--2706.
120. Some curious congruences modulo primes
(with L.-L. Zhao),
J. Number Theory
130(2010), no.4, 930--935.
119. Binomial coefficients, Catalan numbers and Lucas quotients,
Sci. China Math., 53(2010), no.9, 2473--2488.
118. Symmetric identities for Euler polynomials
(with Y. Zhang and H. Pan),
Graphs and Combinatorics 26(2010), no.5, 745--753.
117. New congruences for central binomial coefficients (with R. Tauraso),
Adv. in Appl. Math. 45(2010), no.1, 125--148.
116. 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.
115. 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.
114. On m-covers and m-systems,
Bull. Austral. Math. Soc. 81(2010), no.2, 223--235.
113. Covers of the integers with odd moduli
and their applications to the forms
xm
-2n and
x2
-F3n /2
(with K.-J. Wu),
Math. Comp. 78(2009), no.267, 1853--1866.
112. A new extension of the Erdos-Heilbronn
conjecture (with H. Pan),
J.
Combin. Theory Ser. A 116(2009), no.8, 1374--1381.
111. Mixed sums of squares and triangular number (III) (with B. K. Oh),
J. Number Theory
129(2009), no.4, 964-969.
110. On Bialostocki's conjecture for zero-sum sequences
(with S. Guo),
Acta Arith., 140(2009), no.4, 329--334.
109. On sums of primes and triangular numbers,
Journal of Combinatorics and Number Theory,
1(2009), no.1, 65--76.
arXiv:0803.3737.
108. Zero-sum problems for abelian p-groups
and covers of the integers by residue classes,
Israel J. Math. 170(2009), 235--252.
107. A variant of Tao's method with application to restricted sumsets (with S. Guo),
J. Number Theory
129(2009), no.2, 434-438.
106. An additive theorem and restricted sumsets,
Math. Res. Lett. 15(2008), no.6, 1263-1276.
105. Chinese Edition of the Book: A Friendly Introduction to Number Theory (3rd Ed.)
by J. H. Silverman
(translated with K.-J. Wu, Q.-L. Lu and H.-Q. Cao),
Pearson Education and China Machine Press, 2008.
104. Lucas-type congruences for cyclotomic
ψ-coefficients (with D. Wan),
Int. J. Number Theory 4(2008), no.2, 155--170.
103. On covers of abelian groups by cosets
(with G. Lettl),
Acta Arith.
131(2008), no.4, 341--350.
102. On sums of binomial coefficients and their applications,
Discrete Math.
308(2008), no.18, 4231--4245.
101. On value sets of polynomials over a field,
Finite Fields Appl.
14(2008), no.2, 470--481.
100. Determination of the two-color Rado number
for a1
x1+...
+am
xm
=x0
(with S. Guo),
J.
Combin. Theory Ser. A, 115(2008), no.2, 345--353.
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