{"paper":{"title":"On a ternary Diophantine problem with mixed powers of primes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Alessandro Languasco, Alessandro Zaccagnini","submitted_at":"2012-06-01T17:06:59Z","abstract_excerpt":"Let $1 < k < 33 / 29$. We prove that if $\\lambda_1$, $\\lambda_2$ and $\\lambda_3$ are non-zero real numbers, not all of the same sign and that $\\lambda_1 / \\lambda_2$ is irrational and $\\varpi$ is any real number, then for any $\\eps > 0$ the inequality $ \\bigl|\\lambda_1 p_1 + \\lambda_2 p_2^2 + \\lambda_3 p_3^k + \\varpi \\bigr| \\le \\bigl(\\max_j p_j \\bigr)^{-(33 - 29 k) / (72 k) + \\eps} $ has infinitely many solutions in prime variables $p_1$, ..., $p_k$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1206.0250","kind":"arxiv","version":2},"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"}