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Secondly, we prove that all solutions of this equation in integers $x,y,n$ with $x,y\\geq1, n\\geq2, k\\neq3$ and $l\\equiv0 \\pmod 2$ satisfy $\\max\\{x,y,n\\}<C_{2}$ where $C_{2}$ is an effectively computable constant depending only on $k$ and $l$."},"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":"1701.02466","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2017-01-10T08:12:56Z","cross_cats_sorted":[],"title_canon_sha256":"2df8f52da631f6cd8a99a6a0386d4846a3e04af77412ef29315ed43774a49a46","abstract_canon_sha256":"aaf6d30753fdfec69cf747e0c9069a8dc3627c97578e9f23a179403400836d95"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:53:04.192408Z","signature_b64":"V3EZUg6HeLlb8uxllB0SAznyEKhVLFcaVIoKpewQDngGLgKqACL0ld6u0HjbwtX7xUYq8xW4RzsrgaSiphr0Ag==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"bc965c2a8a036c1df04ab7326bed652fc000a88fc39f434e0d06088513808930","last_reissued_at":"2026-05-18T00:53:04.191741Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:53:04.191741Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On the Diophantine equation $(x+1)^{k}+(x+2)^{k}+...+(lx)^{k}=y^{n}$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"G\\\"okhan Soydan","submitted_at":"2017-01-10T08:12:56Z","abstract_excerpt":"Let $k,l\\geq2$ be fixed integers. In this paper, firstly, we prove that all solutions of the equation $(x+1)^{k}+(x+2)^{k}+...+(lx)^{k}=y^{n}$ in integers $x,y,n$ with $x,y\\geq1, n\\geq2$ satisfy $n<C_{1}$ where $C_{1}=C_{1}(l,k)$ is an effectively computable constant. Secondly, we prove that all solutions of this equation in integers $x,y,n$ with $x,y\\geq1, n\\geq2, k\\neq3$ and $l\\equiv0 \\pmod 2$ satisfy $\\max\\{x,y,n\\}<C_{2}$ where $C_{2}$ is an effectively computable constant depending only on $k$ and $l$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1701.02466","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":"1701.02466","created_at":"2026-05-18T00:53:04.191847+00:00"},{"alias_kind":"arxiv_version","alias_value":"1701.02466v1","created_at":"2026-05-18T00:53:04.191847+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1701.02466","created_at":"2026-05-18T00:53:04.191847+00:00"},{"alias_kind":"pith_short_12","alias_value":"XSLFYKUKANWB","created_at":"2026-05-18T12:31:56.362134+00:00"},{"alias_kind":"pith_short_16","alias_value":"XSLFYKUKANWB34CK","created_at":"2026-05-18T12:31:56.362134+00:00"},{"alias_kind":"pith_short_8","alias_value":"XSLFYKUK","created_at":"2026-05-18T12:31:56.362134+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/XSLFYKUKANWB34CKW4ZGX3LFF7","json":"https://pith.science/pith/XSLFYKUKANWB34CKW4ZGX3LFF7.json","graph_json":"https://pith.science/api/pith-number/XSLFYKUKANWB34CKW4ZGX3LFF7/graph.json","events_json":"https://pith.science/api/pith-number/XSLFYKUKANWB34CKW4ZGX3LFF7/events.json","paper":"https://pith.science/paper/XSLFYKUK"},"agent_actions":{"view_html":"https://pith.science/pith/XSLFYKUKANWB34CKW4ZGX3LFF7","download_json":"https://pith.science/pith/XSLFYKUKANWB34CKW4ZGX3LFF7.json","view_paper":"https://pith.science/paper/XSLFYKUK","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1701.02466&json=true","fetch_graph":"https://pith.science/api/pith-number/XSLFYKUKANWB34CKW4ZGX3LFF7/graph.json","fetch_events":"https://pith.science/api/pith-number/XSLFYKUKANWB34CKW4ZGX3LFF7/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/XSLFYKUKANWB34CKW4ZGX3LFF7/action/timestamp_anchor","attest_storage":"https://pith.science/pith/XSLFYKUKANWB34CKW4ZGX3LFF7/action/storage_attestation","attest_author":"https://pith.science/pith/XSLFYKUKANWB34CKW4ZGX3LFF7/action/author_attestation","sign_citation":"https://pith.science/pith/XSLFYKUKANWB34CKW4ZGX3LFF7/action/citation_signature","submit_replication":"https://pith.science/pith/XSLFYKUKANWB34CKW4ZGX3LFF7/action/replication_record"}},"created_at":"2026-05-18T00:53:04.191847+00:00","updated_at":"2026-05-18T00:53:04.191847+00:00"}