178. On certain determinants and related Legendre symbols (with H. Wang),
Bull. Malays. Math. Sci. Soc., 47 (2024), no. 2, Article No. 58, 19 pages.
177. On some determinants involving the tangent function,
Ramanujan J., in press. arXiv:1901.04837
176. A new trigonometric identity with applications (with H. Pan),
Contrib. Discrete Math., in press.
175. 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.
174. 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.
173. Legendre symbols related to certain determinants (with X.-Q. Luo),
Bull. Malays. Math. Sci. Soc., 46 (2023), no. 4, Article No. 119, 20 pages.
172. Proof of a conjecture involving derangements and roots of unity (with H. Wang),
Electron. J. Combin., 30 (2023), no. 2, #P2.1, 10 pages.
171. A parametri congruence motivated by Orr's identity (with C. Wang),
J. Difference Equ. Appl. 29 (2023), no. 2, 198--207.
170. Some new series for 1/π motivated by congruences,
Colloq. Math. 173 (2023), no. 1, 89--109.
169. On congruences involving Apery numbers (with W. Xia),
Proc. Amer. Math. Soc., in press.
arXiv:2212.09455
168. The tangent function and power residues modulo primes,
Czechoslovak Math. J. , in press. arXiv:2208.05928
167. Trigonometric identities and quadratic residues,
Publ. Math. Debrecen 102 (2023), no. 1-2, 111--138.
166. On practical numbers of some special forms (with L.-Y. Wang),
Houston J. Math. 48 (2022), no. 2, 241--247.
165. 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.
164. On Motzkin numbers and central trinomial coefficients,
Adv. in Appl. Math.
136 (2022), Article ID 102319.
163. Proof of some conjectural hypergeometric supercongruences via curious identities (with C. Wang),
J. Math. Anal. Appl. 505 (2022), Article ID 125575.
162. 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.
161. On sums and products in a field (with G.-L. Zhou),
Czechoslovak. Math. J. 72 (2022), 817--823.
160. Supercongruences involving Lucas sequences,
Monatsh. Math. 196 (2021), 577--606.
159. On permutations of {1,...,n} and related topics,
J. Algebraic Combin. 54 (2021), 893--912.
158. q-Analogues of some series for powers of π (with Q.-H. Hou),
Ann. Comb. 25 (2021), no. 1, 167--177.
157. Further results on Hilbert's Tenth Problem,
Sci. China Math., 64 (2021), no. 2, 281--306.
156. 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.
155. New series for powers of π and related congruences,
Electron. Res. Arch. 28 (2020), no. 3, 1273--1342.
154. 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.
153. Quadratic residues and quartic residues modulo primes,
Int. J. Number Theory 16 (2020), no. 8, 1833--1858.
152. Proof of some conjectures involving quadratic residues (with F. Petrov),
Electron. Res. Arch. 28 (2020), no. 2, 589--597.
151. On sums of four pentagonal numbers with coefficients (with D. Krachun),
Electron. Res. Arch. 28 (2020), no. 1, 559--566.
150. On some determinants involving Jacobi symbols (with D. Krachun, F. Petrov and M. Vsemirnov),
Finite Fields Appl. 64 (2020), Article 101672.
149. On the 1-3-5 conjecture and related topics (with H.-L. Wu),
Acta Arith. 193 (2020), no. 3, 253--268.
148. Universal sums of three quadratic polynomials,
Sci. China Math. 63 (2020), no. 3, 501-520.
147. Some universal quadratic sums over the integers (with H.-L. Wu),
Electron. Res. Arch., 27 (2019), 69-87.
146. Quadratic residues and related permutations and identities,
Finite Fields Appl. 59 (2019), 246--283.
145. Restricted sums of four squares,
Int. J. Number Theory 15 (2019), no. 9, 1863--1893.
144. On some determinants with Legendre symbol entries,
Finite Fields Appl. 56 (2019), 285--307.
143. Consecutive primes and Legendre symbols (with H. Pan),
Acta Arith. 190 (2019), no. 3, 209--220.
142. 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.
141. Two q-analogues of Euler's formula ζ(2)=π2/6,
Colloq. Math. 158 (2019), no. 2, 313--320.
140. New congruences involving products of two binomial coefficients (with G.-S. Mao),
Ramanujan J. 49 (2019), no. 2, 237--256.
139. Divisibility results on Franel numbers and related polynomials (with C. Wang),
Int. J. Number Theory 15 (2019), no. 2, 433--444.
138. Sone variants of Lagrange's four squares theorem (with Y.-C. Sun),
Acta Arith. 183(2018), no.4, 339--356.
137. Hankel-type determinants for some combinatorial sequences (with B.-X. Zhu),
Int. J. Number Theory 14(2018), no.5, 1265-1277.
136. Two new kinds of numbers and related divisibility results,
Colloq. Math. 154(2018), no.2, 241-273.
135. Telescoping method and congruences for
double sums (with Y.-P. Mu),
Int. J. Number Theory 14(2018), no.1, 143-165.
134. Arithmetic properties of Delannoy numbers and Schr\"oder numbers,
J. Number Theory 183(2018), 146-171.
133. Sums of four polygonal numbers with coefficients (with X.-Z. Meng),
Acta Arith. 180(2017), no.3, 229-249.
132. Supercongruences involving dual sequences,
Finite Fields Appl. 46(2017), 179-216.
131. On a permutation problem for finite abelian groups (with. F. Ge),
Electron. J. Combin., 24(2017), no.1, #P1.17, 1-6.
130. Refining Lagrange's four-square theorem,
J. Number Theory 175(2017), 167-190.
[This paper contains my challenging 1-3-5-Conjecture.]
129. 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.
128. A new theorem on the prime-counting function,
Ramanujan J. 42(2017), no.1, 59-67.
127. 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.]
126. A result similar to Lagrange's theorem,
J. Number Theory 162(2016), 190-211.
125. Two congruences involving harmonic numbers with applications (with G.-S. Mao),
Int. J. Number Theory 12(2016), no.2, 527-539.
124. The least modulus for which consecutive polynomial values are distinct,
J. Number Theory 160 (2016), 108-116.
123. 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.
122. On some universal sums of generalized polygonal numbers (with F. Ge),
Colloq. Math. 145(2016), no.1, 149-155.
121. A new series for π^3 and related congruences,
Internat. J. Math. 26 (2015), no.8, 1550055 (23 pages).
120. Proof of a conjectural supercongruence (with X.-Z. Meng),
Finite Fields Appl. 35 (2015), 86-91.
119. Some congruences involving binomial coefficients (with H.-Q. Cao),
Colloq. Math. 139 (2015), no.1, 127-136.
118. On universal sums of polygonal numbers,
Sci. China Math. 58 (2015), no.7, 1367-1396.
117. Supercongruences motivated by e,
J. Number Theory 147 (2015), no.1, 326-341.
116. On monotonicity of some combinatorial sequences (with Q.-H. Hou and H. Wen),
Publ. Math. Debrecen 85 (2014), no.3-4, 285-295.
115. Proof of three conjectures on congruences (with H. Pan),
Sci. China Math. 57 (2014), no.10, 2091-2102.
114. Congruences involving generalized central trinomial coefficients,
Sci. China Math. 57 (2014), no.7, 1375-1400.
113. p-adic congruences motivated by series,
J. Number Theory 134 (2014), no.1, 181-196.
112. 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.
111. Connections between p=x2+3y2
and Franel numbers,
J. Number Theory 133 (2013), no.9, 2914-2928.
110. On functions taking only prime values,
J. Number Theory 133 (2013), no.8, 2794-2812.
[This paper contains many mysterious conjectures on primes.]
109. Supercongruences involving products of two binomial coefficients,
Finite Fields Appl. 22 (2013), 24--44.
108. Fibonacci numbers modulo cubes of primes,
Taiwanese J. Math. 17 (2003), no.5, 1523-1543.
107. Congruences for Franel numbers,
Adv. in Appl. Math. 51 (2013), 524-535.
106. Arithmetic theory of harmonic numbers (II) (with Li-Lu Zhao),
Colloq. Math. 130 (2013), no.1, 67--78.
105. 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]
104. On a sequence involving sums of primes,
Bull. Austral. Math. Soc. 88 (2013), no.2, 197-205.
103. A refinement of a congruence result by van Hamme and Mortenson,
Illinois J. Math. 56 (2012), no.3, 967--979
102. On divisibility of binomial coefficients,
J. Austral. Math. Soc. 93 (2012), 189-201.
101. On sums involving products of three binomial coefficients,
Acta Arith. 156 (2012), no.2, 123-141.
100. On sums of Apery polynomials and related congruences,
J. Number Theory 132 (2012), no.11, 2673-2699.
99. Some q-congruences related to 3-adic valuations (with H. Pan),
Adv. in Appl. Math. 49(2012), no.3-5, 263-270
98. On sums of binomial coefficients modulo
p2,
Colloq. Math. 127(2012), no.1, 39-54.
97. On weighted zero-sum sequences (with S. D. Adhikari and D. J. Grynkiewicz),
Adv. in Appl. Math. 48(2012), no.3, 506--527.
96.Linear extension of the Erdos-Heilbronn conjecture
(with Lilu Zhao),
J.
Combin. Theory Ser. A 119(2012), no.2, 364--381.
95. On harmonic numbers and Lucas sequences,
Math. Publ. Debrecen 80(2012), no.1-2, 25--41.
94. Arithmetic theory of harmonic numbers,
Proc. Amer. Math. Soc. 140(2012), no.2, 415--428.
93. Super congruences and Euler numbers,
Sci. China Math. 54(2011), no.12, 2509--2535.
92. Binomial coefficients and the ring of p-adic integers
(with W. Zhang),
Proc. Amer. Math. Soc. 139(2011), no.5, 1569--1577.
91. On Delannoy numbers and Schroder numbers,
J. Number Theory
131(2011), no.12, 2387-2397.
90. On congruences related to central binomial coefficients,
J. Number Theory
131(2011), no.11, 2219-2238.
89. p-adic valuations of some sums of multinomial coefficients,
Acta Arith.
148(2011), no.1, 63-76.
88. On a curious property of Bell numbers
(with D. Zagier),
Bull. Austral. Math. Soc.
84(2011), no.1, 153-158.
(Initial arXiv version).
87. Exterior algebras and two conjectures on finite abelian groups (with T. Feng and
Q. Xiang),
Israel J. Math. 182(2011), no.1, 425--437.
86. On some new congruences for binomial coefficients (with R. Tauraso),
Int. J. Number Theory 7(2011), no.3, 645--662.
85. On almost universal mixed sums of squares and triangular numbers
(with B. Kane),
Trans. Amer. Math. Soc. 362(2010), no.12, 6425--6455.
84. On 2-adic orders of some binomial sums (with H. Pan),
J. Number Theory 130(2010), no.12, 2701--2706.
83. Some curious congruences modulo primes
(with L.-L. Zhao),
J. Number Theory
130(2010), no.4, 930--935.
82. Binomial coefficients, Catalan numbers and Lucas quotients,
Sci. China Math. 53(2010), no.9, 2473--2488.
81. Symmetric identities for Euler polynomials
(with Y. Zhang and H. Pan),
Graphs and Combinatorics 26(2010), no.5, 745--753.
80. New congruences for central binomial coefficients (with R. Tauraso),
Adv. in Appl. Math. 45(2010), no.1, 125--148.
79. 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.
78. On m-covers and m-systems,
Bull. Austral. Math. Soc. 81(2010), no.2, 223--235.
77. Covers of the integers with odd moduli
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xm
-2n and
x2
-F3n /2
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Math. Comp. 78(2009), no.267, 1853--1866.
76. A new extension of the Erdos-Heilbronn
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J.
Combin. Theory Ser. A 116(2009), no.8, 1374--1381.
75. Mixed sums of squares and triangular number (III) (with B. K. Oh),
J. Number Theory
129(2009), no.4, 964--969.
arXiv:0804.3750.
74. On Bialostocki's conjecture for zero-sum sequences
(with S. Guo),
Acta Arith., 140(2009), no.4, 329--334.
73. Zero-sum problems for abelian p-groups
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Israel J. Math. 170(2009), 235--252.
72. A variant of Tao's method with application to restricted sumsets (with S. Guo),
J. Number Theory
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71. An additive theorem and restricted sumsets,
Math. Res. Lett. 15(2008), no.6, 1263--1276.
70. Lucas-type congruences for cyclotomic
ψ-coefficients (with D. Wan),
Int. J. Number Theory 4(2008), no.2, 155--170.
69. On covers of abelian groups by cosets
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Acta Arith.
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68. On sums of binomial coefficients and their applications,
Discrete Math.
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67. On value sets of polynomials over a field,
Finite Fields Appl.
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66. Determination of the two-color Rado number
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J.
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65. A characterization of covering equivalence (with H. Pan),
Acta Arith.
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64. Congruences for sums of binomial coefficients (with
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J. Number Theory
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63. On Fleck quotients (with D. Wan),
Acta Arith.
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62. A sharp result on m-covers
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Proc. Amer. Math. Soc. 135(2007), no.11, 3515--3520.
61. Combinatorial congruences and
Stirling numbers,
Acta Arith. 126(2007), no.4, 387--398.
60. Combinatorial congruences modulo prime powers
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Trans. Amer. Math. Soc. 359(2007), no.11, 5525--5553.
59. On the number of zero-sum subsequences (with H.-Q. Cao),
Discrete Math.
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58. Mixed sums of squares and triangular numbers,
Acta Arith. 127(2007), no.2, 103--113.
57. A number-theoretic approach to homotopy exponents of SU(n)
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J.
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56. A connection between covers
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Adv. in Appl. Math.
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J. Number Theory
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53. Finite covers of groups by cosets or subgroups,
Internat. J. Math.
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52. A combinatorial identity with application
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Discrete Math.
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51. On the unique representability
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Discrete Math.
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50. On q-Euler numbers, q-Sali\'e numbers and q-Carlitz numbers
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Acta Arith.
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49. Binomial coefficients and quadratic fields,
Proc. Amer. Math. Soc. 134(2006), no.8, 2213--2222.
48. Restricted sumsets and a conjecture of Lev
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Israel J. Math., 154(2006), no.1, 21--28.
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Acta Arith.,
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J.
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45. A local-global theorem on periodic maps,
J. Algebra
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J. Number Theory
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J. Number Theory 111(2005), no.1, 190--196.
MR 2005m:11015.
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MR 2005h:68068.
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Fibonacci Quart. 42(2004), no.4, 295--299.
MR 2006a:11024; Zbl. M. 1064.11019.
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European J. Combin. 24(2003), no.6, 709--718. Zbl. M. 1024.05010.
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Electron.
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Safety verification for two-way finite
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Discrete Math. 262(2003), 253--276. MR 2003m:11037.
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J. Combin. Theory Ser. A 100(2002), no.2, 387--393.
MR 2003k:11016; Zbl. M. 1020.11080.
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26.
On the sum ≡k≡ r (mod m)
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Israel J. Math. 128(2002), 135--156. MR 2003d:11026.
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Discrete Math. 257(2002), no.1, 143--159.
MR 2003g:11037; Zbl. M. 1007.05018.
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Acta Arith. 102(2002), no.3, 239--249.
MR 2003e:11025; Zbl. M. 0988.11008.
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A note on integers of the form
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Proc. Edinburgh Math. Soc. 45(2002), no.1, 155--160. MR 2002j:11117.
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An extension of Lucas' theorem (with H. Hu),
Proc. Amer. Math. Soc. 129(2001), no.12, 3471--3478. MR 2002i:11019.
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Hall's theorem revisited,
Proc. Amer. Math. Soc. 129(2001), no.10, 3129--3131.
MR 2002h:05007; Zbl. M. 0966.05067.
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Acta Arith. 99(2001), no.1, 41--60. MR 2002j:11016; Zbl. M. 0974.11009.
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Fibonacci Quart. 39(2001), no.3, 214--220.
MR 2002d:11016; Zbl. M. 0992.11014.
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European J. Combin. 22(2001), no.3, 415--429.
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Acta Arith. 97(2001), no.1, 87--98.
MR 2002m:11013; Zbl. M. 0986.11009.
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