{"paper":{"title":"Some observations concerning reducibility of quadrinomials","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Andrew Bremner, Maciej Ulas","submitted_at":"2013-10-20T16:55:51Z","abstract_excerpt":"In a recent paper \\cite{Jan}, Jankauskas proved some interesting results concerning the reducibility of quadrinomials of the form $f(4,x)$, where $f(a,x)=x^{n}+x^{m}+x^{k}+a$. He also obtained some examples of reducible quadrinomials $f(a,x)$ with $a\\in\\Z$, such that all the irreducible factors of $f(a,x)$ are of degree $\\geq 3$.\n  In this paper we perform a more systematic approach to the problem and ask about reducibility of $f(a,x)$ with $a\\in\\Q$. In particular by computing the set of rational points on some genus two curves we characterize in several cases all quadrinomials $f(a,x)$ with d"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1310.5346","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"}