{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2018:NKBVHMIH3SERNSM3UH7T6SXLQZ","short_pith_number":"pith:NKBVHMIH","schema_version":"1.0","canonical_sha256":"6a8353b107dc8916c99ba1ff3f4aeb867350e51a1b27f7f007e391ef0e9276e2","source":{"kind":"arxiv","id":"1812.08705","version":1},"attestation_state":"computed","paper":{"title":"A certain reciprocal power sum is never an integer","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Junyong Zhao, Shaofang Hong, Xiao Jiang","submitted_at":"2018-12-20T17:11:47Z","abstract_excerpt":"By $(\\mathbb{Z}^+)^{\\infty}$ we denote the set of all the infinite sequences $\\mathcal{S}=\\{s_i\\}_{i=1}^{\\infty}$ of positive integers (note that all the $s_i$ are not necessarily distinct and not necessarily monotonic). Let $f(x)$ be a polynomial of nonnegative integer coefficients. Let $\\mathcal{S}_n:=\\{s_1, ..., s_n\\}$ and $H_f(\\mathcal{S}_n):=\\sum_{k=1}^{n}\\frac{1}{f(k)^{s_{k}}}$. When $f(x)$ is linear, Feng, Hong, Jiang and Yin proved in [A generalization of a theorem of Nagell, Acta Math. Hungari, in press] that for any infinite sequence $\\mathcal{S}$ of positive integers, $H_f(\\mathcal{"},"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":"1812.08705","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2018-12-20T17:11:47Z","cross_cats_sorted":[],"title_canon_sha256":"b5bd74c87b1ba9a60186be5f3d6f3d57484c89bcef5648c200faf2c5a6d00f77","abstract_canon_sha256":"fd51bf073268536ed867a11df1804a9a0fdc71ac19b0d1d30a55a38802b249d5"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:57:49.347668Z","signature_b64":"eVQJmvr5/ZoTsXttN6eL+Nf4X5nKSZR+cQfMul/esVPtJLD2Yjtp2GEJLBZMUdqBj86Unfi9yepHkjWxT3WwCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"6a8353b107dc8916c99ba1ff3f4aeb867350e51a1b27f7f007e391ef0e9276e2","last_reissued_at":"2026-05-17T23:57:49.347087Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:57:49.347087Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"A certain reciprocal power sum is never an integer","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Junyong Zhao, Shaofang Hong, Xiao Jiang","submitted_at":"2018-12-20T17:11:47Z","abstract_excerpt":"By $(\\mathbb{Z}^+)^{\\infty}$ we denote the set of all the infinite sequences $\\mathcal{S}=\\{s_i\\}_{i=1}^{\\infty}$ of positive integers (note that all the $s_i$ are not necessarily distinct and not necessarily monotonic). Let $f(x)$ be a polynomial of nonnegative integer coefficients. Let $\\mathcal{S}_n:=\\{s_1, ..., s_n\\}$ and $H_f(\\mathcal{S}_n):=\\sum_{k=1}^{n}\\frac{1}{f(k)^{s_{k}}}$. When $f(x)$ is linear, Feng, Hong, Jiang and Yin proved in [A generalization of a theorem of Nagell, Acta Math. Hungari, in press] that for any infinite sequence $\\mathcal{S}$ of positive integers, $H_f(\\mathcal{"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1812.08705","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"aliases":[{"alias_kind":"arxiv","alias_value":"1812.08705","created_at":"2026-05-17T23:57:49.347193+00:00"},{"alias_kind":"arxiv_version","alias_value":"1812.08705v1","created_at":"2026-05-17T23:57:49.347193+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1812.08705","created_at":"2026-05-17T23:57:49.347193+00:00"},{"alias_kind":"pith_short_12","alias_value":"NKBVHMIH3SER","created_at":"2026-05-18T12:32:40.477152+00:00"},{"alias_kind":"pith_short_16","alias_value":"NKBVHMIH3SERNSM3","created_at":"2026-05-18T12:32:40.477152+00:00"},{"alias_kind":"pith_short_8","alias_value":"NKBVHMIH","created_at":"2026-05-18T12:32:40.477152+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/NKBVHMIH3SERNSM3UH7T6SXLQZ","json":"https://pith.science/pith/NKBVHMIH3SERNSM3UH7T6SXLQZ.json","graph_json":"https://pith.science/api/pith-number/NKBVHMIH3SERNSM3UH7T6SXLQZ/graph.json","events_json":"https://pith.science/api/pith-number/NKBVHMIH3SERNSM3UH7T6SXLQZ/events.json","paper":"https://pith.science/paper/NKBVHMIH"},"agent_actions":{"view_html":"https://pith.science/pith/NKBVHMIH3SERNSM3UH7T6SXLQZ","download_json":"https://pith.science/pith/NKBVHMIH3SERNSM3UH7T6SXLQZ.json","view_paper":"https://pith.science/paper/NKBVHMIH","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1812.08705&json=true","fetch_graph":"https://pith.science/api/pith-number/NKBVHMIH3SERNSM3UH7T6SXLQZ/graph.json","fetch_events":"https://pith.science/api/pith-number/NKBVHMIH3SERNSM3UH7T6SXLQZ/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/NKBVHMIH3SERNSM3UH7T6SXLQZ/action/timestamp_anchor","attest_storage":"https://pith.science/pith/NKBVHMIH3SERNSM3UH7T6SXLQZ/action/storage_attestation","attest_author":"https://pith.science/pith/NKBVHMIH3SERNSM3UH7T6SXLQZ/action/author_attestation","sign_citation":"https://pith.science/pith/NKBVHMIH3SERNSM3UH7T6SXLQZ/action/citation_signature","submit_replication":"https://pith.science/pith/NKBVHMIH3SERNSM3UH7T6SXLQZ/action/replication_record"}},"created_at":"2026-05-17T23:57:49.347193+00:00","updated_at":"2026-05-17T23:57:49.347193+00:00"}