{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T16:44:01Z","timestamp":1753893841067,"version":"3.41.2"},"reference-count":0,"publisher":"The Electronic Journal of Combinatorics","issue":"4","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Electron. J. Combin."],"abstract":"<jats:p>We pose the question of determining the lowest-degree polynomial with nonnegative coefficients divisible by the $n$-th cyclotomic polynomial $\\Phi_n(x)$.\u00a0We show this polynomial is $1 + x^{n\/p} + \\cdots + x^{(p-1)n\/p}$ where $p$ is the smallest prime dividing $n$ whenever $2\/p &gt; 1\/q_1 + \\cdots + 1\/q_k$, where $q_1, \\ldots, q_k$ are the other (distinct) primes besides $p$ dividing $n$.\u00a0Determining the lowest-degree polynomial with nonnegative coefficients divisible by $\\Phi_n(x)$ remains open in the general case, though we conjecture the existence of values of $n$ for which this degree is, in fact, less than $(p-1)n\/p$.<\/jats:p>","DOI":"10.37236\/2755","type":"journal-article","created":{"date-parts":[[2020,1,10]],"date-time":"2020-01-10T22:12:30Z","timestamp":1578694350000},"source":"Crossref","is-referenced-by-count":2,"title":["The Lowest-Degree Polynomial with Nonnegative Coefficients Divisible by the $n$-th Cyclotomic Polynomial"],"prefix":"10.37236","volume":"19","author":[{"given":"John P.","family":"Steinberger","sequence":"first","affiliation":[]}],"member":"23455","published-online":{"date-parts":[[2012,10,18]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v19i4p1\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v19i4p1\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,1,17]],"date-time":"2020-01-17T17:28:53Z","timestamp":1579282133000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v19i4p1"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2012,10,18]]},"references-count":0,"journal-issue":{"issue":"4","published-online":{"date-parts":[[2012,10,18]]}},"URL":"https:\/\/doi.org\/10.37236\/2755","relation":{},"ISSN":["1077-8926"],"issn-type":[{"type":"electronic","value":"1077-8926"}],"subject":[],"published":{"date-parts":[[2012,10,18]]},"article-number":"P1"}}