Ramanujan-type congruences modulo 4 for partitions into distinct parts
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⋅n+p2-124)≡0 (mod4),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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| Format: | Article |
| Language: | English |
| Published: |
Sciendo
2022-09-01
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| Series: | Analele Stiintifice ale Universitatii Ovidius Constanta: Seria Matematica |
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| Online Access: | https://doi.org/10.2478/auom-2022-0040 |
| _version_ | 1811194309570985984 |
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| author | Merca Mircea |
| author_facet | Merca Mircea |
| author_sort | Merca Mircea |
| collection | DOAJ |
| description | 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⋅n+p2-124)≡0 (mod4),Q\left( {p \cdot n + {{{p^2} - 1} \over {24}}} \right) \equiv 0\,\,\,\left( {\bmod 4} \right),
where p ⩾ 5 is a prime. |
| first_indexed | 2024-04-12T00:23:44Z |
| format | Article |
| id | doaj.art-cf171f6c77f843f3a63cc42391bb62f0 |
| institution | Directory Open Access Journal |
| issn | 1844-0835 |
| language | English |
| last_indexed | 2024-04-12T00:23:44Z |
| publishDate | 2022-09-01 |
| publisher | Sciendo |
| record_format | Article |
| series | Analele Stiintifice ale Universitatii Ovidius Constanta: Seria Matematica |
| spelling | doaj.art-cf171f6c77f843f3a63cc42391bb62f02022-12-22T03:55:36ZengSciendoAnalele Stiintifice ale Universitatii Ovidius Constanta: Seria Matematica1844-08352022-09-0130318519910.2478/auom-2022-0040Ramanujan-type congruences modulo 4 for partitions into distinct partsMerca Mircea0Department of Mathematical Methods and Models, University POLITEHNICA of Bucharest, Splaiul Independentei 313, 060042Bucharest, Romania.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⋅n+p2-124)≡0 (mod4),Q\left( {p \cdot n + {{{p^2} - 1} \over {24}}} \right) \equiv 0\,\,\,\left( {\bmod 4} \right), where p ⩾ 5 is a prime.https://doi.org/10.2478/auom-2022-0040partitionscongruencesdivisorsprimary 11p83secondary 11p81; 11p82 |
| spellingShingle | Merca Mircea Ramanujan-type congruences modulo 4 for partitions into distinct parts Analele Stiintifice ale Universitatii Ovidius Constanta: Seria Matematica partitions congruences divisors primary 11p83 secondary 11p81; 11p82 |
| title | Ramanujan-type congruences modulo 4 for partitions into distinct parts |
| title_full | Ramanujan-type congruences modulo 4 for partitions into distinct parts |
| title_fullStr | Ramanujan-type congruences modulo 4 for partitions into distinct parts |
| title_full_unstemmed | Ramanujan-type congruences modulo 4 for partitions into distinct parts |
| title_short | Ramanujan-type congruences modulo 4 for partitions into distinct parts |
| title_sort | ramanujan type congruences modulo 4 for partitions into distinct parts |
| topic | partitions congruences divisors primary 11p83 secondary 11p81; 11p82 |
| url | https://doi.org/10.2478/auom-2022-0040 |
| work_keys_str_mv | AT mercamircea ramanujantypecongruencesmodulo4forpartitionsintodistinctparts |