{"paper":{"title":"The Diophantine Equation arctan(1/x)+arctan(m/y)= arctan(1/k)","license":"http://creativecommons.org/licenses/by/3.0/","headline":"","cross_cats":[],"primary_cat":"math.GM","authors_text":"Konstantine Zelator","submitted_at":"2012-03-28T21:13:22Z","abstract_excerpt":"In the fall 2011 issue of the Journal'Mathematics and Computer Education', author Unal Hasan, in the one page article \"Proof without Words\", gives a purely geometric proof of the equality, arctan(1/3)+ arctan(1/7) = arctan(1/2) (1) (See reference [1]) Now consider the two-variable diophantine equation(x and y being positive integer variables), arctan(1/x) + arctan(m/y) = arctan(1/k) (2), where m and k are given or fixed positive integers with gcd(m,k^2+1)=1;and also with gcd(m,y)=1. Equality (1) then says that the pair (3,7)is a positive integer solution to (2) in the case m=1=k. We prove, in "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1203.6380","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"}