{"paper":{"title":"On 3 and 9-regular cubic partitions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"D. S. Gireesh, M. S. Mahadeva Naika, Shivashankar C","submitted_at":"2019-07-01T11:53:55Z","abstract_excerpt":"Let $a_3(n)$ and $a_9(n)$ are 3 and 9-regular cubic partitions of $n$. In this paper, we find the infinite family of congruences modulo powers of 3 for $a_3(n)$ and $a_9(n)$ such as \\[a_3\\left (3^{2\\alpha}n+\\frac{3^{2\\alpha}-1}{4}\\right )\\equiv 0 \\pmod{3^{\\alpha}}\\] and \\[a_9\\left (3^{\\alpha+1}n+3^{\\alpha+1}-1\\right )\\equiv 0 \\pmod{3^{\\alpha+1}}.\\]"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1907.00674","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}