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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 "},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1203.6380","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/3.0/","primary_cat":"math.GM","submitted_at":"2012-03-28T21:13:22Z","cross_cats_sorted":[],"title_canon_sha256":"4456ea49a64a5769aa949291cbbd7d0a825823cb39245f44b486ab5a8c433c1b","abstract_canon_sha256":"f7c9c766fc66c38ff0e5cd0a15aa86de04a52ff1297756cd42efc2dbdf07167c"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:59:02.669130Z","signature_b64":"v6TXwXJQl2SmVwG8FPUKzgb97DIl0X/WTchh/NcvPgLAZQ4Mb/nX7LIPO2KW1Q4UHxsByHwBKOBm8lwWZOzOCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"3c0061edb878227b114bb66c8c2f65a7d60a1f13a04d920ababfa1e491b073f2","last_reissued_at":"2026-05-18T03:59:02.668401Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:59:02.668401Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"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. 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