A CONJECTURE OF MERCA ON CONGRUENCES MODULO POWERS OF 2 FOR PARTITIONS INTO DISTINCT PARTS
| Autor: | JULIA Q. D. DU, DAZHAO TANG |
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| Rok vydání: | 2023 |
| Předmět: | |
| Zdroj: | Bulletin of the Australian Mathematical Society. :1-11 |
| ISSN: | 1755-1633 0004-9727 |
| DOI: | 10.1017/s0004972723000229 |
| Popis: | Let $Q(n)$ denote the number of partitions of n into distinct parts. Merca [‘Ramanujan-type congruences modulo 4 for partitions into distinct parts’, An. Şt. Univ. Ovidius Constanţa30(3) (2022), 185–199] derived some congruences modulo $4$ and $8$ for $Q(n)$ and posed a conjecture on congruences modulo powers of $2$ enjoyed by $Q(n)$ . We present an approach which can be used to prove a family of internal congruence relations modulo powers of $2$ concerning $Q(n)$ . As an immediate consequence, we not only prove Merca’s conjecture, but also derive many internal congruences modulo powers of $2$ satisfied by $Q(n)$ . Moreover, we establish an infinite family of congruence relations modulo $4$ for $Q(n)$ . |
| Databáze: | OpenAIRE |
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