Supercongruences involving Domb numbers and binary quadratic forms

Guo-Shuai Mao; Michael J. Schlosser

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arXiv · 2112.12732

Supercongruences involving Domb numbers and binary quadratic forms

Guo-Shuai Mao·Michael J. Schlosser

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Abstract

In this paper, we prove two recently conjectured supercongruences (modulo $p^3$, where $p$ is any prime greater than $3$) of Zhi-Hong Sun on truncated sums involving the Domb numbers. Our proofs involve a number of ingredients such as congruences involving specialized Bernoulli polynomials, harmonic numbers, binomial coefficients, and hypergeometric summations and transformations.

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Guo-Shuai Mao, Michael J. Schlosser. 2021-12-23. Supercongruences involving Domb numbers and binary quadratic forms. https://arxiv.org/abs/2112.12732

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