Congruences for the Almkvist-Zudilin numbers

2014/06/24 by Amdeberhan, Tewodros
#FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.1406.6343

Abstract

Given a prime number p, the study of divisibility properties of a sequence c(n) has two contending approaches: p-adic valuations and superconcongruences. The former searches for the highest power of p dividing c(n), for each n; while the latter (essentially) focuses on the maximal powers r and t such that c(p^rn) is congruent to c(p^r-1n) modulo p^t. This is called supercongruence. In this note, we prove modest supercongruences for certain sequences that have come to be known as the Almkvist-Zudilin numbers and two other naturally related ones.

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