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We further show that the average number of non-torsion integral points in this family is bounded above by $2$. As an application we also deduce from our upper bounds that the system of simultaneous Pell equations $aX^2-bY^2=d$, $bY^2-cZ^2=d$ for pairwise coprime positive inte"},"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":"2004.03331","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2020-04-07T13:10:06Z","cross_cats_sorted":[],"title_canon_sha256":"7068db7f77f8681a1a316205a7e0315dd7255a22ffddc9380322e4ce59065c11","abstract_canon_sha256":"bbc7bd7aa9981f64b86c7877eaffa3ac20c5aa6985577cd73e0f295bf93f3eba"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T05:15:07.982585Z","signature_b64":"dSkaBiW1se1t1o27R3Q4Du/K5bMaEHakcgcOgdicKaWfRZ93MoqPJKU/+p66id+/fbiF+FFJEAvJti87AGUVAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ddca804c56d07641cc6e28fc15045bd74c8bd77faa723117dc2e47263140e8d4","last_reissued_at":"2026-07-05T05:15:07.982113Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T05:15:07.982113Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Integral points on the congruent number curve","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Stephanie Chan","submitted_at":"2020-04-07T13:10:06Z","abstract_excerpt":"We study integral points on the quadratic twists $\\mathcal{E}_D:y^2=x^3-D^2x$ of the congruent number curve. 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