{"paper":{"title":"Triples which are $D(n)$-sets for several $n$'s","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Andrej Dujella, Dijana Kreso, Nikola Ad\\v{z}aga, Petra Tadi\\'c","submitted_at":"2017-03-30T20:15:26Z","abstract_excerpt":"For a nonzero integer $n$, a set of distinct nonzero integers $\\{a_1,a_2,\\ldots,a_m\\}$ such that $a_ia_j+n$ is a perfect square for all $1\\leq i<j\\leq m$, is called a Diophantine $m$-tuple with the property $D(n)$ or simply $D(n)$-set. $D(1)$-sets are known as simply Diophantine $m$-tuples. Such sets were first studied by Diophantus of Alexandria, and since then by many authors. It is natural to ask if there exists a Diophantine $m$-tuple ($D(1)$-set) which is also a $D(n)$-set for some $n\\neq 1$. This question was raised by Kihel and Kihel in 2001. They conjectured that there are no Diophanti"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1703.10659","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"}