Some new q -congruences for truncated double basic hypergeometric sums

In this paper, by virtue of a very-well-poised 6ϕ5 summation and a quadratic summation of Gasper and Rahman, we establish four new q-congruences involving double sums. As a conclusion, we obtain the following supercongruence: for any prime p≡3(mod4) and p>3, ∑k=0(p+1)/2(6k−1)(12)k(−14)k2k!34k∑j=1k{1(4j−5)2−14j2}≡0(modp2), where (a)n=a(a+1)⋯(a+n−1). In addition, we put forward two conjectures on congruences to inspire further research.

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Publication Details

Journal
The Journal of Difference Equations and Applications
Published
2026-09-12
DOI
https://doi.org/10.1080/10236198.2026.2727008
Primary Topic
Advanced Mathematical Identities
Type
article
Field-Weighted Citation Impact
0.00

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article

Some new q -congruences for truncated double basic hypergeometric sums

Long Li
The Journal of Difference Equations and Applications
Advanced Mathematical Identities
article

Some new q -congruences for truncated double basic hypergeometric sums

Long Li
article en

Abstract

In this paper, by virtue of a very-well-poised 6ϕ5 summation and a quadratic summation of Gasper and Rahman, we establish four new q-congruences involving double sums. As a conclusion, we obtain the following supercongruence: for any prime p≡3(mod4) and p>3, ∑k=0(p+1)/2(6k−1)(12)k(−14)k2k!34k∑j=1k{1(4j−5)2−14j2}≡0(modp2), where (a)n=a(a+1)⋯(a+n−1). In addition, we put forward two conjectures on congruences to inspire further research.

The Journal of Difference Equations and Applications
Huaiyin Normal University (CN)
Qinglan Project of Jiangsu Province of China
Openalex Percentile: Top 4%
Advanced Mathematical Identities
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