{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2013:7UXWPP672TK5PNLDXIMYFLQTPV","short_pith_number":"pith:7UXWPP67","schema_version":"1.0","canonical_sha256":"fd2f67bfdfd4d5d7b563ba1982ae137d6e459fcf649f9cafdc0d1c09ce866f55","source":{"kind":"arxiv","id":"1308.4040","version":1},"attestation_state":"computed","paper":{"title":"Integer Solutions, Rational solutions of the equations x^4+y^4+z^4 -2(x^2)(y^2)-2(y^2)(z^2)-2(z^2)(x^2)=n and x^2+y^4+z^4-2x(y^2)-2x(z^2)-2(y^2)(z^2)=n; And Crux Mathematicorum Contest problem CC24","license":"http://creativecommons.org/licenses/by/3.0/","headline":"","cross_cats":[],"primary_cat":"math.GM","authors_text":"Konstantine Zelator","submitted_at":"2013-08-16T16:51:14Z","abstract_excerpt":"The subject matter of this work are the two equations: x^4+y^4+z^4-2(x^2)(y^2)-2(y^2)(z^2)-2(z^2)(x^2)= n (1) And x^2+y^4+z^4-2x(y^2)-2x(z^2)-2(y^4)(z^4)= n (2) where n is a natural number.\n  Contest Corner problem CC24, published in the May2012 issue of the journal Crux Mathematicorum(see reference[1]); provided the motivation behind this work. In Th.1, we show that eq.(1) if n=8N, N odd; then eq.(1) has no integer solutions; which generalizes problem CC24(the case n=24).\n  We use Th.2, to find some rational solutions of eq.(1); which answers the second question in CC24. In Th.4, we show that"},"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":"1308.4040","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/3.0/","primary_cat":"math.GM","submitted_at":"2013-08-16T16:51:14Z","cross_cats_sorted":[],"title_canon_sha256":"1f10cab1bcd832f5ae8434007f06146e57e8c6b26bfb15dc45dfcf191b456cd6","abstract_canon_sha256":"07dfe08246d2b86c395cb48243f4873f0c9e7f10ca3242eb9e0963d6db94c11e"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:15:35.029858Z","signature_b64":"/+zPzwEDhph/gBrday8qZaBk0qm91SGToCie6OAUvVLD2DwFhiBFGoMDjz+QpElS2Uhr4x3Qf8C6DGWzK+gmBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"fd2f67bfdfd4d5d7b563ba1982ae137d6e459fcf649f9cafdc0d1c09ce866f55","last_reissued_at":"2026-05-18T03:15:35.029255Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:15:35.029255Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Integer Solutions, Rational solutions of the equations x^4+y^4+z^4 -2(x^2)(y^2)-2(y^2)(z^2)-2(z^2)(x^2)=n and x^2+y^4+z^4-2x(y^2)-2x(z^2)-2(y^2)(z^2)=n; And Crux Mathematicorum Contest problem CC24","license":"http://creativecommons.org/licenses/by/3.0/","headline":"","cross_cats":[],"primary_cat":"math.GM","authors_text":"Konstantine Zelator","submitted_at":"2013-08-16T16:51:14Z","abstract_excerpt":"The subject matter of this work are the two equations: x^4+y^4+z^4-2(x^2)(y^2)-2(y^2)(z^2)-2(z^2)(x^2)= n (1) And x^2+y^4+z^4-2x(y^2)-2x(z^2)-2(y^4)(z^4)= n (2) where n is a natural number.\n  Contest Corner problem CC24, published in the May2012 issue of the journal Crux Mathematicorum(see reference[1]); provided the motivation behind this work. In Th.1, we show that eq.(1) if n=8N, N odd; then eq.(1) has no integer solutions; which generalizes problem CC24(the case n=24).\n  We use Th.2, to find some rational solutions of eq.(1); which answers the second question in CC24. 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