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By elementary means, we show that the $D(-8k^2)$-pair $\\{8k^2, 8k^2+1\\}$ can be extended to at most a quadruple (the third and fourth element can only be $1$ and $32k^2+1$). At the end, we suggest considering a $D(-k^2)$-triple $\\{ 1, 2k^2, 2k^2+2k+1\\}$ as possible future research direction."},"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":"1610.04415","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2016-10-14T11:52:02Z","cross_cats_sorted":[],"title_canon_sha256":"77fbbe03bf3b700abeadd7d5c8b57913f89cd347052f7bed184666bf9869305e","abstract_canon_sha256":"b11715b25a0913385cb76728ec5d521a255b78f64a266c63286a44006e728bc9"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:39:18.212626Z","signature_b64":"K7WfgX9I09OtqcFs+M3Emmiq1ohKXMUE1Xzrn/32ebTxMtW12v08KNPLseblQ8gp0JWdC6NQUNt0zkywSEHqDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"01349ea0b7ca91a9180349df7b1f4550b5720afd92b98de186f69e8d26911543","last_reissued_at":"2026-05-18T00:39:18.212009Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:39:18.212009Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On the extension of $D(-8k^2)$-pair $\\{8k^2, 8k^2+1\\}$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Alan Filipin, Nikola Ad\\v{z}aga","submitted_at":"2016-10-14T11:52:02Z","abstract_excerpt":"Let $n$ be a nonzero integer. 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