On a conjectured \(q\)-congruence of Guo and Zeng. (English) Zbl 1428.11041


11B65 Binomial coefficients; factorials; \(q\)-identities
11A07 Congruences; primitive roots; residue systems
05A10 Factorials, binomial coefficients, combinatorial functions
05A30 \(q\)-calculus and related topics
Full Text: DOI


[1] Andrews, G. E., The Theory of Partitions, (1998), Cambridge University Press, Cambridge · Zbl 0996.11002
[2] Guo, V. J. W.; Pan, H.; Zhang, Y., The rodriguez-villegas type congruences for truncated \(q\)-hypergeometric functions, J. Number Theory, 174, 358-368, (2017) · Zbl 1387.11018
[3] Guo, V. J. W.; Zeng, J., Some \(q\)-analogues of supercongruences of rodriguez-villegas, J. Number Theory, 145, 301-316, (2014) · Zbl 1315.11015
[4] Guo, V. J. W.; Zeng, J., Some \(q\)-supercongruences for truncated basic hypergeometric series, Acta Arith., 1171, 309-326, (2015) · Zbl 1338.11024
[5] Mortenson, E., A supercongruence conjecture of rodriguez-villegas for a certain truncated hypergeometric function, J. Number Theory, 199, 139-147, (2003) · Zbl 1074.11045
[6] Mortenson, E., Supercongruences between truncated \({}_2 F_1\) hypergeometric functions and their Gaussian analogs, Trans. Amer. Math. Soc., 1355, 987-1007, (2003) · Zbl 1074.11044
[7] Rodriguez-Villegas, F., Calabi-Yau Varieties and Mirror Symmetry, 38, Hypergeometric families of Calabi-Yau manifolds, 223-231, (2003), American Mathematical Society, Providence, RI · Zbl 1062.11038
[8] Sun, Z.-H., Generalized Legendre polynomials and related supercongruences, J. Number Theory, 143, 293-319, (2014) · Zbl 1353.11005
[9] Sun, Z.-H., Supecongruences involving products of two binomial coefficients, Finite Fields Appl., 122, 24-44, (2013) · Zbl 1331.11012
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.