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We offer our own proof of this result in Proposition1.Using Proposition1 and Lemma2, we establish Proposition 2: Let a,b,c be positive reals. Then a triangle ABC having a,b,c as its sidelengths can be formed if,and onlyif, b^2=a(a+c) and either c<(or equal to)a; or alternatively a<c<3a. Now, consider the case of integral triangles, that is; a,b, and c bieng positive 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":"1208.0497","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/3.0/","primary_cat":"math.GM","submitted_at":"2012-08-01T17:28:55Z","cross_cats_sorted":[],"title_canon_sha256":"8a6453e43d401bc8aebbd1ca5836d803781f7c6ef2ebce593392bfa5184bab81","abstract_canon_sha256":"4bf9e34538cf650db4248d38c3a876b314dfff3ca1478154e83a183d8f9c2dd2"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:49:34.016808Z","signature_b64":"eZ26U4vF+PVoKzfZube78Y09MNbtBZGFrn7luRcdFDNgjuTUo9pqqx3irZHgXMAlmK9qq4Fw2OcdVTBohozFCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"157cfa5af9402e16955ee56c916ba7a9a2248ddebf1c61b2c54e243455443ef7","last_reissued_at":"2026-05-18T03:49:34.016165Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:49:34.016165Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Integral Triangles with one angle twice another, and with the bisector(of the double angle) also of integral length","license":"http://creativecommons.org/licenses/by/3.0/","headline":"","cross_cats":[],"primary_cat":"math.GM","authors_text":"Konstantine Zelator","submitted_at":"2012-08-01T17:28:55Z","abstract_excerpt":"Let ABC be a triangle with a,b,and c being its three sidelengths. 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