{"paper":{"title":"Reciprocal Properties of Pythagorean triangles","license":"http://creativecommons.org/licenses/by/3.0/","headline":"","cross_cats":[],"primary_cat":"math.GM","authors_text":"Konstantine Zelator","submitted_at":"2011-10-02T19:16:21Z","abstract_excerpt":"Let (a,b,c)be a Pythagorean triple with c being the hypotenuse length, and h being the altitude to the hypotenuse. Also, let v,k,l be positive integers with k and l being relatively prime.We say(Definition1 in this work)that the Pythagorean triple (a,b,c) has the reciprocal property R(v,k,l)if the positive integers a,b,c,v,k,and l satisfy the condition or equation, 1/a+1/b+v/h = k/l. The motivating force behind this work, is a problem that appeared in the journal, Crux Mathematicorum with Mathematical Mayhem. The said problem is Mayhem problem M390, and it appeared in the April2009 issue of th"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1110.0217","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"}