{"paper":{"title":"Notes On a Borwein and Choi's conjecture of cyclotomic polynomials with coefficients $\\pm1$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Shaofang Hong, Wei Cao","submitted_at":"2018-07-31T07:49:11Z","abstract_excerpt":"Borwein and Choi conjectured that a polynomial $P(x)$ with coefficients $\\pm1$ of degree $N-1$ is cyclotomic iff $$P(x)=\\pm \\Phi_{p_1}(\\pm x)\\Phi_{p_2}(\\pm x^{p_1})\\cdots \\Phi_{p_r}(\\pm x^{p_1p_2\\cdots p_{r-1}})$$ where $N=p_1p_2\\cdots p_{r}$ and the $p_i$ are primes, not necessarily distinct. Here $\\Phi_p(x):=(x^p-1)/(x-1)$ is the $p-$th cyclotomic polynomial. In \\cite{1}, they also proved the conjecture for $N$ odd or a power of 2. In this paper we introduce a so-called $E-$transformation, by which we prove the conjecture for a wider variety of cases and present the key as well as a new appr"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1807.11693","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"}