{"paper":{"title":"Detecting lacunary perfect powers and computing their roots","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.SC","authors_text":"Daniel S. Roche, Mark Giesbrecht","submitted_at":"2009-01-13T18:44:43Z","abstract_excerpt":"We consider solutions to the equation f = h^r for polynomials f and h and integer r > 1. Given a polynomial f in the lacunary (also called sparse or super-sparse) representation, we first show how to determine if f can be written as h^r and, if so, to find such an r. This is a Monte Carlo randomized algorithm whose cost is polynomial in the number of non-zero terms of f and in log(deg f), i.e., polynomial in the size of the lacunary representation, and it works over GF(q)[x] (for large characteristic) as well as Q[x]. We also give two deterministic algorithms to compute the perfect root h give"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0901.1848","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"}