{"paper":{"title":"A Diophantine problem with prime variables","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Alessandro Languasco, Alessandro Zaccagnini","submitted_at":"2012-06-01T17:14:55Z","abstract_excerpt":"We study the distribution of the values of the form $\\lambda_1 p_1 + \\lambda_2 p_2 + \\lambda_3 p_3^k$, where $\\lambda_1$, $\\lambda_2$ and $\\lambda_3$ are non-zero real number not all of the same sign, with $\\lambda_1 / \\lambda_2$ irrational, and $p_1$, $p_2$ and $p_3$ are prime numbers. We prove that, when $1 < k < 4 / 3$, these value approximate rather closely any prescribed real number."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1206.0252","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"}