{"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"}