On a conjectured q-congruence of Guo and Zeng

DOI10.1142/S1793042118501038zbMath1428.11041MaRDI QIDQ3174675

Hao Pan, He-Xia Ni

Publication date: 17 July 2018

Published in: International Journal of Number Theory (Search for Journal in Brave)

zbMATH Keywords

\(q\)-binomial coefficientcongruencecyclotomic polynomial\(q\)-Chu-Vandermonde identity

Mathematics Subject Classification ID

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

Related Items (28)

Proof of two conjectures of Guo and Schlosser ⋮ Factors of some truncated basic hypergeometric series ⋮ Some \(q\)-supercongruences from Watson's \(_8\phi_7\) transformation formula ⋮ A common \(q\)-analogue of two supercongruences ⋮ Proof of some \(q\)-supercongruences modulo the fourth power of a cyclotomic polynomial ⋮ Some generalizations of a congruence by Sun and Tauraso ⋮ \(q\)-supercongruences from squares of basic hypergeometric series ⋮ Further generalizations of four supercongruences of Rodriguez-Villegas ⋮ Proof of some supercongruences through a \(q\)-microscope ⋮ Some new \(q\)-congruences on double sums ⋮ A family of \(q\)-hypergeometric congruences modulo the fourth power of a cyclotomic polynomial ⋮ Dwork-type supercongruences through a creative \(q\)-microscope ⋮ A q-analogue of the (A.2) supercongruence of Van Hamme for any prime p ≡ 3(mod4) ⋮ \(q\)-analogues of the (G.2) supercongruence of Van Hamme ⋮ Proof of a \(q\)-supercongruence conjectured by Guo and Schlosser ⋮ \(q\)-analogues of two Ramanujan-type supercongruences ⋮ Some \(q\)-supercongruences modulo the fourth power of a cyclotomic polynomial ⋮ A further \(q\)-analogue of Van Hamme's (H.2) supercongruence for any prime \(p\equiv 1\pmod{4}\) ⋮ Some new \(q\)-congruences for truncated basic hypergeometric series: even powers ⋮ On two conjectural supercongruences of Z.-W. Sun ⋮ Some new \(q\)-congruences for truncated basic hypergeometric series ⋮ Common \(q\)-analogues of some different supercongruences ⋮ Some \(q\)-supercongruences from a quadratic transformation by Rahman ⋮ Some $q$-congruences with parameters ⋮ Some q-supercongruences for truncated forms of squares of basic hypergeometric series ⋮ Some q-congruences on double basic hypergeometric sums ⋮ Further \(q\)-analogues of the (G.2) supercongruence of Van Hamme ⋮ A $q$-congruence for a truncated $_4\varphi_3$ series

Cites Work

• Unnamed Item
• Unnamed Item
• The Rodriguez-Villegas type congruences for truncated \(q\)-hypergeometric functions
• Generalized Legendre polynomials and related supercongruences
• Some \(q\)-analogues of supercongruences of Rodriguez-Villegas
• A supercongruence conjecture of Rodriguez-Villegas for a certain truncated hypergeometric function.
• Supercongruences involving products of two binomial coefficients
• Some q-supercongruences for truncated basic hypergeometric series
• Supercongruences between truncated $_{2}F_{1}$ hypergeometric functions and their Gaussian analogs

This page was built for publication: On a conjectured q-congruence of Guo and Zeng