{"paper":{"title":"A variant of Waring's Problem for the ring of integers modulo n","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Alex Iosevich, David Covert, Jonathan Pakianathan","submitted_at":"2016-09-07T17:49:22Z","abstract_excerpt":"We study a variant of Waring's problem for $\\mathbb{Z}_n$, the ring of integers modulo $n$: For a fixed integer $k \\geq 2$, what is the minimum number $m$ of $k$th powers necessary such that $x \\equiv x_1^k + \\dots + x_m^k \\pmod{n}$ has a solution for every $x \\in \\mathbb{Z}_n$? Using only elementary methods, we answer fully this question for exponents $k \\leq 10$, and we further discuss some intermediary cases such as categorizing the values of $n$ such that every element in $\\mathbb{Z}_n$ can be written as a sum of three squares. Hensel's Theorem for $p$-adic integers plays a key role. Final"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1609.02090","kind":"arxiv","version":2},"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"}