{"paper":{"title":"Sums of two cubes as twisted perfect powers, revisited","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Carmen Bruni, Michael A. Bennett, Nuno Freitas","submitted_at":"2017-02-25T03:26:35Z","abstract_excerpt":"In this paper, we sharpen earlier work of the first author, Luca and Mulholland, showing that the Diophantine equation $$ A^3+B^3 = q^\\alpha C^p, \\, \\, ABC \\neq 0, \\, \\, \\gcd (A,B) =1, $$ has, for \"most\" primes $q$ and suitably large prime exponents $p$, no solutions. We handle a number of (presumably infinite) families where no such conclusion was hitherto known. Through further application of certain {\\it symplectic criteria}, we are able to make some conditional statements about still more values of $q$, a sample such result is that, for all but $O(\\sqrt{x}/\\log x)$ primes $q$ up to $x$, th"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1702.07827","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"}