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In this paper, we find all integers $ c $ having at least two representations as a difference between: a Fibonacci number and a power of $ 3 $; a Padovan number and a"},"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":"1902.03491","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2019-02-09T21:18:27Z","cross_cats_sorted":[],"title_canon_sha256":"f0349a610c7493e854bb9b8450117f3c98fc1475668e979a7ead67918d3efa76","abstract_canon_sha256":"176fd8d0da7db341d82cd8768be7e5fd8a712e3bc8fa4cc8adbae8dbfef06df5"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:44:42.503274Z","signature_b64":"zBgTIwb2w91ApbGVrYbEiIdXt/V2z62WDmbPAo3GExKL9NCNOhgPGH5AtmmSl84LHj+yHysoYCqY6GliD+/+CA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"03e194a2ec2032e6eeb6e65ab165360c40bd337f9ebbd1ca65b5f68025827902","last_reissued_at":"2026-05-17T23:44:42.502644Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:44:42.502644Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On the problem of Pillai with Fibonacci numbers, Padovan numbers, and Tribonacci numbers and powers of $3$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Mahadi Ddamulira","submitted_at":"2019-02-09T21:18:27Z","abstract_excerpt":"Consider the sequences: $ \\{F_{n}\\}_{n\\geq 0} $ of Fibonacci numbers defined by $ F_0=0 $, $ F_1 =1$ and $ F_{n+2}=F_{n+1}+ F_{n} $ for all $ n\\geq 0 $; $ \\{P_{n}\\}_{n\\geq 0} $ of Padovan numbers defined by $ P_0=0 $, $ P_1 =1 = P_2 $ and $ P_{n+3}=P_{n+1}+ P_{n} $ for all $ n\\geq 0 $; and $ \\{T_{n}\\}_{n\\geq 0} $ of Tribonacci numbers defined by $ T_0=0 $, $ T_1 =1= T_2$ and $ T_{n+3}=T_{n_2}+T_{n+1}+ T_{n} $ for all $ n\\geq 0 $. In this paper, we find all integers $ c $ having at least two representations as a difference between: a Fibonacci number and a power of $ 3 $; a Padovan number and a"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1902.03491","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":""},"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":"1902.03491","created_at":"2026-05-17T23:44:42.502755+00:00"},{"alias_kind":"arxiv_version","alias_value":"1902.03491v3","created_at":"2026-05-17T23:44:42.502755+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1902.03491","created_at":"2026-05-17T23:44:42.502755+00:00"},{"alias_kind":"pith_short_12","alias_value":"APQZJIXMEAZO","created_at":"2026-05-18T12:33:12.712433+00:00"},{"alias_kind":"pith_short_16","alias_value":"APQZJIXMEAZON3VW","created_at":"2026-05-18T12:33:12.712433+00:00"},{"alias_kind":"pith_short_8","alias_value":"APQZJIXM","created_at":"2026-05-18T12:33:12.712433+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/APQZJIXMEAZON3VW4ZNLCZJWBR","json":"https://pith.science/pith/APQZJIXMEAZON3VW4ZNLCZJWBR.json","graph_json":"https://pith.science/api/pith-number/APQZJIXMEAZON3VW4ZNLCZJWBR/graph.json","events_json":"https://pith.science/api/pith-number/APQZJIXMEAZON3VW4ZNLCZJWBR/events.json","paper":"https://pith.science/paper/APQZJIXM"},"agent_actions":{"view_html":"https://pith.science/pith/APQZJIXMEAZON3VW4ZNLCZJWBR","download_json":"https://pith.science/pith/APQZJIXMEAZON3VW4ZNLCZJWBR.json","view_paper":"https://pith.science/paper/APQZJIXM","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1902.03491&json=true","fetch_graph":"https://pith.science/api/pith-number/APQZJIXMEAZON3VW4ZNLCZJWBR/graph.json","fetch_events":"https://pith.science/api/pith-number/APQZJIXMEAZON3VW4ZNLCZJWBR/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/APQZJIXMEAZON3VW4ZNLCZJWBR/action/timestamp_anchor","attest_storage":"https://pith.science/pith/APQZJIXMEAZON3VW4ZNLCZJWBR/action/storage_attestation","attest_author":"https://pith.science/pith/APQZJIXMEAZON3VW4ZNLCZJWBR/action/author_attestation","sign_citation":"https://pith.science/pith/APQZJIXMEAZON3VW4ZNLCZJWBR/action/citation_signature","submit_replication":"https://pith.science/pith/APQZJIXMEAZON3VW4ZNLCZJWBR/action/replication_record"}},"created_at":"2026-05-17T23:44:42.502755+00:00","updated_at":"2026-05-17T23:44:42.502755+00:00"}