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Recently Wu, She and Ni proved that $(\\frac{D_p(1,1)}p)=(\\frac {-2}p)$ if $p\\equiv2\\pmod 3$, which confirms a previous conjecture of Sun. In this paper we determine $(\\frac{D_p(1,1)}p)$ in the case $p\\equiv1\\pmod3$. Sun proved that $D_p(2,2)\\equiv0\\pmod p$ if $p\\equiv3\\pmod4$, in contrast we prove that $(\\frac{D_p(2,2)}p)=1$ if $p\\equiv1\\pmod8$, and $(\\frac{D_p(2,2)}p)=0$ if $p\\eq"},"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":"2210.14741","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2022-10-26T14:19:47Z","cross_cats_sorted":[],"title_canon_sha256":"7f133c8fc260a21de0e46c37dd9d4ccc63ab4644430ba292369ad753d1250e92","abstract_canon_sha256":"1902f60d13791eeeadff01c0139a3a262492c53cba994b184b5aa4c4cb2cc8c6"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T06:11:42.940729Z","signature_b64":"yWia4Mfv35uY2zIM778wr6HR13dxabHPHZT5bINUQl9+VC6nQDYJXnwVNrKomIfIGJNnxNq2fNawFvyNts+7AA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"14d26e7b082a21ad7576846823244a282e545a1c2851a1ca8dfbf4a6c1eaae40","last_reissued_at":"2026-07-05T06:11:42.940253Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T06:11:42.940253Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Legendre symbols related to certain determinants","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Xin-Qi Luo, Zhi-Wei Sun","submitted_at":"2022-10-26T14:19:47Z","abstract_excerpt":"Let $p$ be an odd prime. 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Sun proved that $D_p(2,2)\\equiv0\\pmod p$ if $p\\equiv3\\pmod4$, in contrast we prove that $(\\frac{D_p(2,2)}p)=1$ if $p\\equiv1\\pmod8$, and $(\\frac{D_p(2,2)}p)=0$ if $p\\eq"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2210.14741","kind":"arxiv","version":3},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2210.14741/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2210.14741","created_at":"2026-07-05T06:11:42.940325+00:00"},{"alias_kind":"arxiv_version","alias_value":"2210.14741v3","created_at":"2026-07-05T06:11:42.940325+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2210.14741","created_at":"2026-07-05T06:11:42.940325+00:00"},{"alias_kind":"pith_short_12","alias_value":"CTJG46YIFIQ2","created_at":"2026-07-05T06:11:42.940325+00:00"},{"alias_kind":"pith_short_16","alias_value":"CTJG46YIFIQ225LW","created_at":"2026-07-05T06:11:42.940325+00:00"},{"alias_kind":"pith_short_8","alias_value":"CTJG46YI","created_at":"2026-07-05T06:11:42.940325+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/CTJG46YIFIQ225LWQRUCGJCKFA","json":"https://pith.science/pith/CTJG46YIFIQ225LWQRUCGJCKFA.json","graph_json":"https://pith.science/api/pith-number/CTJG46YIFIQ225LWQRUCGJCKFA/graph.json","events_json":"https://pith.science/api/pith-number/CTJG46YIFIQ225LWQRUCGJCKFA/events.json","paper":"https://pith.science/paper/CTJG46YI"},"agent_actions":{"view_html":"https://pith.science/pith/CTJG46YIFIQ225LWQRUCGJCKFA","download_json":"https://pith.science/pith/CTJG46YIFIQ225LWQRUCGJCKFA.json","view_paper":"https://pith.science/paper/CTJG46YI","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2210.14741&json=true","fetch_graph":"https://pith.science/api/pith-number/CTJG46YIFIQ225LWQRUCGJCKFA/graph.json","fetch_events":"https://pith.science/api/pith-number/CTJG46YIFIQ225LWQRUCGJCKFA/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/CTJG46YIFIQ225LWQRUCGJCKFA/action/timestamp_anchor","attest_storage":"https://pith.science/pith/CTJG46YIFIQ225LWQRUCGJCKFA/action/storage_attestation","attest_author":"https://pith.science/pith/CTJG46YIFIQ225LWQRUCGJCKFA/action/author_attestation","sign_citation":"https://pith.science/pith/CTJG46YIFIQ225LWQRUCGJCKFA/action/citation_signature","submit_replication":"https://pith.science/pith/CTJG46YIFIQ225LWQRUCGJCKFA/action/replication_record"}},"created_at":"2026-07-05T06:11:42.940325+00:00","updated_at":"2026-07-05T06:11:42.940325+00:00"}