{"paper":{"title":"Five squares in arithmetic progression over quadratic fields","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Enrique Gonz\\'alez-Jim\\'enez, Xavier Xarles","submitted_at":"2009-09-09T09:59:59Z","abstract_excerpt":"We give several criteria to show over which quadratic number fields Q(sqrt{D}) there should exists a non-constant arithmetic progressions of five squares. This is done by translating the problem to determining when some genus five curves C_D defined over Q have rational points, and then using a Mordell-Weil sieve argument among others. Using a elliptic Chabauty-like method, we prove that the only non-constant arithmetic progressions of five squares over Q(sqrt{409}), up to equivalence, is 7^2, 13^2, 17^2, 409, 23^2. Furthermore, we give an algorithm that allow to construct all the non-constant"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0909.1663","kind":"arxiv","version":4},"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"}