Zhi-Wei Sun's Publications (2008-)  [Preprints, 2000-2007, 1987-1999, SCI papers]
193. Restricted sums of four squares,
  Int. J. Number Theory, accepted. arXiv:1701.05868
192. On some determinants with Legendre symbol entries,
  Finite Fields Appl. 56(2019), 285--307.
191. Universal sums of three quadratic polynomials,
  Sci. China Math., accepted. arXiv:1502.03056
190. Consecutive primes and Legendre symbols (with H. Pan),
  Acta Arith., accepted. arXiv:1406.5951
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., accepted. arXiv:1802.01473
187. New congruences involving products of two binomial coefficients (with G.-S. Mao),
  Ramanujan J., to appear. arXiv:1601.04782
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 (ゞ児粥方胎秘壇〃), Press of Harbin Institute of Technology (込櫛鴛垢匍寄僥竃井芙), 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.