Congruences for Domb and Almkvist-Zudilin numbers
Zhi-Hong Sun
TL;DR
This paper establishes new transformation formulas for congruences modulo primes and derives related congruences for Domb and Almkvist-Zudilin numbers, also proposing conjectures on higher prime power congruences.
Contribution
It introduces novel transformation formulas and congruences for special number sequences, and suggests conjectures for prime power cases.
Findings
Derived new congruences for Domb numbers
Established transformation formulas for congruences
Proposed conjectures on prime power congruences
Abstract
In this paper we prove some transformation formulae for congruences modulo a prime and deduce some congruences for Domb numbers and Almkvist-Zudilin numbers. We also pose some conjectures on congruences modulo prime powers.
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Taxonomy
TopicsAdvanced Mathematical Identities · Advanced Combinatorial Mathematics · Analytic Number Theory Research