{"paper":{"title":"Finiteness results for Diophantine triples with repdigit values","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Attila B\\'erczes, Florian Luca, Istv\\'an Pink, Volker Ziegler","submitted_at":"2015-02-19T12:32:44Z","abstract_excerpt":"Let $g\\ge 2$ be an integer and $\\mathcal R_g\\subset \\mathbb N$ be the set of repdigits in base $g$. Let $\\mathcal D_g$ be the set of Diophantine triples with values in $\\mathcal R_g$; that is, $\\mathcal D_g$ is the set of all triples $(a,b,c)\\in \\mathbb N^3$ with $c<b<a$ such that $ab+1,ac+1$ and $ab+1$ lie in the set $\\mathcal R_g$. In this paper, we prove effective finitness results for the set $\\mathcal D_g$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1502.05550","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"}