Ramanujan-type congruences modulo 4 for partitions into distinct parts

Mircea Merca

doi:10.2478/auom-2022-0040

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Ramanujan-type congruences modulo 4 for partitions into distinct parts

Analele ştiinţifice ale Universităţii "Ovidius" Constanţa. Seria Matematică

Volume 30 (2022): Issue 3 (September 2022)

By: Mircea Merca

Open Access

|Oct 2022

Abstract

In this paper, we consider the partition function Q(n) counting the partitions of n into distinct parts and investigate congruence identities of the form $Q (p \cdot n + \frac{p^{2} - 1}{24}) \equiv 0 (mod 4),$ Q\left( {p \cdot n + {{{p^2} - 1} \over {24}}} \right) \equiv 0\,\,\,\left( {\bmod 4} \right), where p ⩾ 5 is a prime.

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