{"paper":{"title":"Additional congruence conditions on the number of terms in sums of consecutive squared integers equal to squared integers","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.NT"],"primary_cat":"math.HO","authors_text":"Vladimir Pletser","submitted_at":"2014-08-20T22:11:23Z","abstract_excerpt":"The problem of finding all the integer solutions in $a$, $M$ and $s$ of sums of $M$ consecutive integer squares starting at $a^{2}\\geq1$ equal to squared integers $s^{2}$, has no solutions if $M\\equiv3,5,6,7,8$ or $10\\left(mod\\,12\\right)$ and has integer solutions if $M\\equiv0,9,24% or %33\\left(mod\\,72\\right)$; or $M\\equiv1,2$ or $16\\left(mod\\,24\\right)$; or $M\\equiv11\\left(mod\\,12\\right)$. In this paper, additional congruence conditions are demonstrated on the allowed values of $M$ that yield solutions to the problem by using Beeckmans' eight necessary conditions, refining further the possibl"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1409.6261","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"}