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Chen and Xia proved this conjecture by using the $(p,k)$-parametrization of theta functions given by Alaca, Alaca and Williams. In this paper, we show that $\\overline{p}(5n)\\equiv (-1)^{n}\\overline{p}(4\\cdot 5n) \\pmod{5}$ for $n \\geq 0$ and $\\overline{p}(n)\\equiv (-1)^{n}\\overline{p}(4n)\\pmod{8}$ for $n \\geq 0$ by using the relation of the generating function o"},"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":"1406.3801","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2014-06-15T08:29:45Z","cross_cats_sorted":["math.NT"],"title_canon_sha256":"da49aec28c43772bdc4f23eaef2e178cee525c544bb9dfd9dbe1569851f2edc6","abstract_canon_sha256":"2d9c245d2a2b57b5ac85dae767f0cda4ed6ce486d5264607c8d3a76e7b648f55"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:49:39.698983Z","signature_b64":"+j9bWrzeCyriQIW8Ku3DYiI+Fp+L23HQllzMVlGsdP5pkTuHWG0fdBTVYaSqGrhJS86Ld9PKMNpMXChwnd9oAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"693c6c6828f214ed3a481fe867069353551198128ce9ecd01ea63c1aa1cc7e71","last_reissued_at":"2026-05-18T02:49:39.698655Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:49:39.698655Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Ramanujan-type Congruences for Overpartitions Modulo 5","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.NT"],"primary_cat":"math.CO","authors_text":"Lisa H. Sun, Li Zhang, Rong-Hua Wang, William Y.C. Chen","submitted_at":"2014-06-15T08:29:45Z","abstract_excerpt":"Let $\\overline{p}(n)$ denote the number of overpartitions of $n$. Hirschhorn and Sellers showed that $\\overline{p}(4n+3)\\equiv 0 \\pmod{8}$ for $n\\geq 0$. They also conjectured that $\\overline{p}(40n+35)\\equiv 0 \\pmod{40}$ for $n\\geq 0$. Chen and Xia proved this conjecture by using the $(p,k)$-parametrization of theta functions given by Alaca, Alaca and Williams. In this paper, we show that $\\overline{p}(5n)\\equiv (-1)^{n}\\overline{p}(4\\cdot 5n) \\pmod{5}$ for $n \\geq 0$ and $\\overline{p}(n)\\equiv (-1)^{n}\\overline{p}(4n)\\pmod{8}$ for $n \\geq 0$ by using the relation of the generating function o"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1406.3801","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":"1406.3801","created_at":"2026-05-18T02:49:39.698709+00:00"},{"alias_kind":"arxiv_version","alias_value":"1406.3801v1","created_at":"2026-05-18T02:49:39.698709+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1406.3801","created_at":"2026-05-18T02:49:39.698709+00:00"},{"alias_kind":"pith_short_12","alias_value":"NE6GY2BI6IKO","created_at":"2026-05-18T12:28:41.024544+00:00"},{"alias_kind":"pith_short_16","alias_value":"NE6GY2BI6IKO2OSI","created_at":"2026-05-18T12:28:41.024544+00:00"},{"alias_kind":"pith_short_8","alias_value":"NE6GY2BI","created_at":"2026-05-18T12:28:41.024544+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":0,"sample":[{"citing_arxiv_id":"2604.10738","citing_title":"Accessing gluon GTMD $F^g_{1,4}$ via the $\\langle\\sin(2\\phi)\\rangle$ azimuthal asymmetry of exclusive $\\pi^0$ production in $ep$ collisions","ref_index":16,"is_internal_anchor":false}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/NE6GY2BI6IKO2OSID7UGOBUTKN","json":"https://pith.science/pith/NE6GY2BI6IKO2OSID7UGOBUTKN.json","graph_json":"https://pith.science/api/pith-number/NE6GY2BI6IKO2OSID7UGOBUTKN/graph.json","events_json":"https://pith.science/api/pith-number/NE6GY2BI6IKO2OSID7UGOBUTKN/events.json","paper":"https://pith.science/paper/NE6GY2BI"},"agent_actions":{"view_html":"https://pith.science/pith/NE6GY2BI6IKO2OSID7UGOBUTKN","download_json":"https://pith.science/pith/NE6GY2BI6IKO2OSID7UGOBUTKN.json","view_paper":"https://pith.science/paper/NE6GY2BI","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1406.3801&json=true","fetch_graph":"https://pith.science/api/pith-number/NE6GY2BI6IKO2OSID7UGOBUTKN/graph.json","fetch_events":"https://pith.science/api/pith-number/NE6GY2BI6IKO2OSID7UGOBUTKN/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/NE6GY2BI6IKO2OSID7UGOBUTKN/action/timestamp_anchor","attest_storage":"https://pith.science/pith/NE6GY2BI6IKO2OSID7UGOBUTKN/action/storage_attestation","attest_author":"https://pith.science/pith/NE6GY2BI6IKO2OSID7UGOBUTKN/action/author_attestation","sign_citation":"https://pith.science/pith/NE6GY2BI6IKO2OSID7UGOBUTKN/action/citation_signature","submit_replication":"https://pith.science/pith/NE6GY2BI6IKO2OSID7UGOBUTKN/action/replication_record"}},"created_at":"2026-05-18T02:49:39.698709+00:00","updated_at":"2026-05-18T02:49:39.698709+00:00"}