{"paper":{"title":"On decompositions of quadrinomials and related Diophantine equations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Maciej Gawron","submitted_at":"2015-12-09T11:28:19Z","abstract_excerpt":"Let $A,B,C,D$ be rational numbers such that $ABC \\neq 0$, and let $n_1>n_2>n_3>0$ be positive integers. We solve the equation\n  $$ Ax^{n_1}+Bx^{n_2}+Cx^{n_3}+D = f(g(x)),$$ in $f,g \\in \\mathbb{Q}[x]$. In sequel we use Bilu-Tichy method to prove finitness of integral solutions of the equations $$ Ax^{n_1}+Bx^{n_2}+Cx^{n_3}+D = Ey^{m_1}+Fy^{m_2}+Gy^{m_3}+H, $$ where $A,B,C,D,E,F,G,H$ are rational numbers $ABCEFG \\neq 0$ and $n_1>n_2>n_3>0$, $m_1>m_2>m_3>0$, $\\gcd(n_1,n_2,n_3) = \\gcd(m_1,m_2,m_3)=1$ and $n_1,m_1 \\geq 9$. And the equation $$ A_1x^{n_1}+A_2x^{n_2}+\\ldots+A_l x^{n_l} + A_{l+1} = Ey^"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1512.02817","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"}