A TRUNCATED IDENTITY OF EULER AND RELATED -CONGRUENCES

DOI10.1017/S0004972720000301zbMath1453.05013OpenAlexW3016002730MaRDI QIDQ5138949

Unnamed Author, Ji-Cai Liu

Publication date: 4 December 2020

Published in: Bulletin of the Australian Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1017/s0004972720000301

zbMATH Keywords

\(q\)-Catalan numberspentagonal number theorem\(q\)-congruences

Mathematics Subject Classification ID

Combinatorial identities, bijective combinatorics (05A19) (q)-calculus and related topics (05A30) Binomial coefficients; factorials; (q)-identities (11B65) Congruences; primitive roots; residue systems (11A07)

Related Items (19)

A variation of the \(q\)-Wolstenholme theorem ⋮ Explicit formulas and recurrence relations for generalized Catalan numbers ⋮ \(q\)-supercongruences from squares of basic hypergeometric series ⋮ On the divisibility of \(q\)-trinomial coefficients ⋮ Unnamed Item ⋮ Two \(q\)-congruences involving double basic hypergeometric sums ⋮ Supercongruences arising from transformations of hypergeometric series ⋮ Proof of a \(q\)-supercongruence conjectured by Guo and Schlosser ⋮ Supercongruences for sums involving Domb numbers ⋮ \(q\)-analogues of two Ramanujan-type supercongruences ⋮ Some \(q\)-supercongruences modulo the square and cube of a cyclotomic polynomial ⋮ On two supercongruences for sums of Apéry-like numbers ⋮ On two supercongruences of double binomial sums ⋮ Factors of certain sums involving central \(q\)-binomial coefficients ⋮ Some supercongruences arising from symbolic summation ⋮ Some q-supercongruences for truncated forms of squares of basic hypergeometric series ⋮ A \(q\)-supercongruence from a \(q\)-analogue of Whipple's \({}_3F_2\) summation formula ⋮ On the divisibility of sums of even powers of \(q\)-binomial coefficients ⋮ Truncations of Gauss' square exponent theorem

Cites Work

• Unnamed Item
• \(q\)-analogs of some congruences involving Catalan numbers
• The truncated pentagonal number theorem
• Multiple extensions of a finite Euler's pentagonal number theorem and the Lucas formulas
• q-Catalan numbers
• A \(q\)-microscope for supercongruences
• Congruences on sums of \(q\)-binomial coefficients
• Common \(q\)-analogues of some different supercongruences
• $q$-analogues of two supercongruences of Z.-W. Sun
• Some finite generalizations of Euler's pentagonal number theorem
• A Short Proof of an Identity of Euler

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