{"paper":{"title":"Fermat's polygonal number theorem for repeated generalized polygonal numbers","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"math.NT","authors_text":"Ben Kane, Dayoon Park, Hiu Chun So, Manav Batavia, Muratzhan Kyranbay, Piyush Varyani, Sagnik Saha, Soumyarup Banerjee","submitted_at":"2019-08-06T12:17:33Z","abstract_excerpt":"In this paper, we consider sums of generalized polygonal numbers with repeats, generalizing Fermat's polygonal number theorem which was proven by Cauchy. In particular, we obtain the minimal number of generalized $m$-gonal numbers required to represent every positive integer and we furthermore generalize this result to obtain optimal bounds when many of the generalized $m$-gonal numbers are repeated $r$ times, where $r\\in\\mathbb{N}$ is fixed."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1908.02102","kind":"arxiv","version":4},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/1908.02102/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}