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We also prove that there are infinitely many practical numbers of the form $q^4+2$ with $q$ practical, and that there are infinitely many practical Pythagorean triples $(a,b,c)$ with $\\gcd(a,b,c)=6$ (or $\\gcd(a,b,c)=4$)."},"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":"1809.01532","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2018-09-03T15:53:26Z","cross_cats_sorted":[],"title_canon_sha256":"d3ec0b1d5c2fb86fcf9fed706e9e8c61c2b833d7b7fb49a97fe70ea16cfafb2b","abstract_canon_sha256":"f9d62f5294dfe43acd68c8e1488d65ab654ab70f0e18642edfcdf9eacf59d6de"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:40:55.889206Z","signature_b64":"b6JmFUaz4fGZ/tJ4nSrghozKtrTt3SUDy9D3hezt9X0Jc+yKA+FTb+ayxE8Nznt5OJy4UBZ2KuuJfxwbITpOBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"970d2ab5165568451082905a07fcc954c0b219e47b6ea1a8ce987631d21a27b9","last_reissued_at":"2026-05-17T23:40:55.888426Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:40:55.888426Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On practical numbers of some special forms","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Li-Yuan Wang, Zhi-Wei Sun","submitted_at":"2018-09-03T15:53:26Z","abstract_excerpt":"In this paper we study practical numbers of some special forms. 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