{"paper":{"title":"General solutions of sums of consecutive cubed integers equal to squared integers","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Vladimir Pletser","submitted_at":"2015-01-24T23:38:16Z","abstract_excerpt":"All integer solutions $\\left(M,a,c\\right)$ to the problem of the sums of $M$ consecutive cubed integers $\\left(a+i\\right)^{3}$ ($a>1$, $0\\leq i\\leq M-1$) equaling squared integers $c^{2}$ are found by decomposing the product of the difference and sum of the triangular numbers of $\\left(a+M-1\\right)$ and $\\left(a-1\\right)$ in the product of their greatest common divisor $g$ and remaining square factors $\\delta^{2}$ and $\\sigma^{2}$, yielding $c=g\\delta\\sigma$. Further, the condition that $g$ must be integer for several particular and general cases yield generalized Pell equations whose solution"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1501.06098","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"}