{"paper":{"title":"Rational points on certain quintic hypersurfaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Maciej Ulas","submitted_at":"2008-10-01T16:58:08Z","abstract_excerpt":"Let $f(x)=x^5+ax^3+bx^2+cx \\in \\Z[x]$ and consider the hypersurface of degree five given by the equation \\cal{V}_{f}: f(p)+f(q)=f(r)+f(s). Under the assumption $b\\neq 0$ we show that there exists $\\Q$-unirational elliptic surface contained in $\\cal{V}_{f}$. If $b=0, a<0$ and $-a\\not\\equiv 2,18,34 \\pmod {48}$ then there exists $\\Q$-rational surface contained in $\\cal{V}_{f}$. Moreover, we prove that for each $f$ of degree five there exists $\\Q(i)$-rational surface contained in $\\cal{V}_{f}$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0810.0225","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"}