{"paper":{"title":"On the Diophantine equations of the form $\\lambda_1U_{n_1} + \\lambda_2U_{n_2} +\\ldots + \\lambda_kU_{n_k} = wp_1^{z_1}p_2^{z_2} \\cdots p_s^{z_s}$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Brian Ha, Eva Goedhart, Lily McBeath, Luisa Velasco","submitted_at":"2022-12-22T18:24:55Z","abstract_excerpt":"In this paper, we consider the Diophantine equation $\\lambda_1U_{n_1}+\\ldots+\\lambda_kU_{n_k}=wp_1^{z_1} \\cdots p_s^{z_s},$ where $\\{U_n\\}_{n\\geq 0}$ is a fixed non-degenerate linear recurrence sequence of order greater than or equal to 2; $w$ is a fixed non-zero integer; $p_1,\\dots,p_s$ are fixed, distinct prime numbers; $\\lambda_1,\\dots,\\lambda_k$ are strictly positive integers; and $n_1,\\dots,n_k,z_1,\\dots,z_s$ are non-negative integer unknowns. We prove the existence of an effectively computable upper-bound on the solutions $(n_1,\\dots,n_k,z_1,\\dots,z_s)$.\n  In our proof, we use lower boun"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2212.11945","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2212.11945/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"}