{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:CEWMNIVSIF7LBIOS262YA445C2","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"00f72a624cf9572830f8419cca6c45c20bbba4d0449e749529e6b7f62d5e2ec3","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2016-09-15T19:59:24Z","title_canon_sha256":"23c5683b4beb26e4b5dc5e5aad49909140a27597f682763d284aa80be6185172"},"schema_version":"1.0","source":{"id":"1609.04807","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1609.04807","created_at":"2026-05-18T00:23:57Z"},{"alias_kind":"arxiv_version","alias_value":"1609.04807v1","created_at":"2026-05-18T00:23:57Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1609.04807","created_at":"2026-05-18T00:23:57Z"},{"alias_kind":"pith_short_12","alias_value":"CEWMNIVSIF7L","created_at":"2026-05-18T12:30:09Z"},{"alias_kind":"pith_short_16","alias_value":"CEWMNIVSIF7LBIOS","created_at":"2026-05-18T12:30:09Z"},{"alias_kind":"pith_short_8","alias_value":"CEWMNIVS","created_at":"2026-05-18T12:30:09Z"}],"graph_snapshots":[{"event_id":"sha256:aeda7db40b63c0b898e181ac8bb81f91e7b1bf83f44bbc51c5ad461f9fdefacb","target":"graph","created_at":"2026-05-18T00:23:57Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"abstract_excerpt":"Let $N_q$ be the number of solutions to the equation $$ (a_1^{}x_1^{m_1}+\\dots+a_n^{}x_n^{m_n})^k=bx_1^{k_1}\\cdots x_n^{k_n} $$ over the finite field $\\mathbb F_q=\\mathbb F_{p^s}$. Carlitz found formulas for~$N_q$ when $k_1=\\dots=k_n=m_1=\\dots=m_n=1$, $k=2$, $n=3$ or $4$, $p>2$; and when ${m_1=\\dots=m_n=2}$, $k=k_1=\\dots=k_n=1$, $n=3$ or $4$, $p>2$. In earlier papers, we studied the above equation with $k_1=\\dots=k_n=1$ and obtained some generalizations of Carlitz's results. Recently, Pan, Zhao and Cao considered the case of arbitrary positive integers $k_1,\\dots,k_n$ and proved the formula $N","authors_text":"Ioulia N. Baoulina","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2016-09-15T19:59:24Z","title":"On two problems of Carlitz and their generalizations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1609.04807","kind":"arxiv","version":1},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:93ff6bd510dfc1f1daa2e908b8bdb2e4db8a5826ef30ec9e359902f531048972","target":"record","created_at":"2026-05-18T00:23:57Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"00f72a624cf9572830f8419cca6c45c20bbba4d0449e749529e6b7f62d5e2ec3","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2016-09-15T19:59:24Z","title_canon_sha256":"23c5683b4beb26e4b5dc5e5aad49909140a27597f682763d284aa80be6185172"},"schema_version":"1.0","source":{"id":"1609.04807","kind":"arxiv","version":1}},"canonical_sha256":"112cc6a2b2417eb0a1d2d7b580739d16af5dbf7cde7eb145e6f9aa4f1d465b18","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"112cc6a2b2417eb0a1d2d7b580739d16af5dbf7cde7eb145e6f9aa4f1d465b18","first_computed_at":"2026-05-18T00:23:57.072699Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:23:57.072699Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"4+Ju0i9+P5xyyeKbwrQyeWEVnRwSa1TZwErABdq57oDCFKA01dxyQ3A5z4LOFXsAXvA6Xs7pwngImxnizB1mDg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:23:57.073130Z","signed_message":"canonical_sha256_bytes"},"source_id":"1609.04807","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:93ff6bd510dfc1f1daa2e908b8bdb2e4db8a5826ef30ec9e359902f531048972","sha256:aeda7db40b63c0b898e181ac8bb81f91e7b1bf83f44bbc51c5ad461f9fdefacb"],"state_sha256":"209dbc41f646c7d15ebd535b132da846d5bedf5933636c95e5d9b9d53210a38e"}