{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T16:43:45Z","timestamp":1753893825907,"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>Given a prime number $p$, we deduce from a formula of Barsky and Benzaghou and from a result of Coulter and Henderson on trinomials over finite fields, a simple necessary and sufficient condition $\\beta(n) =k\\beta(0)$ in $\\mathbb{F}_{p^p}$\u00a0in order to resolve the congruence $B(n) \\equiv k \\pmod{p}$, where $B(n)$ is the $n$-th Bell number, and $k$\u00a0is any fixed integer. Several applications of the formula and of the condition\u00a0are included, in particular we give equivalent forms of\u00a0the conjecture of Kurepa that\u00a0$B(p-1)$ is $\\neq 1$ modulo $p$.<\/jats:p>","DOI":"10.37236\/3532","type":"journal-article","created":{"date-parts":[[2020,1,10]],"date-time":"2020-01-10T19:33:57Z","timestamp":1578684837000},"source":"Crossref","is-referenced-by-count":0,"title":["Bell Numbers Modulo a Prime Number, Traces and Trinomials"],"prefix":"10.37236","volume":"21","author":[{"given":"Luis H.","family":"Gallardo","sequence":"first","affiliation":[]},{"given":"Olivier","family":"Rahavandrainy","sequence":"additional","affiliation":[]}],"member":"23455","published-online":{"date-parts":[[2014,12,4]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v21i4p49\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v21i4p49\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,1,17]],"date-time":"2020-01-17T05:39:28Z","timestamp":1579239568000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v21i4p49"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2014,12,4]]},"references-count":0,"journal-issue":{"issue":"4","published-online":{"date-parts":[[2014,10,2]]}},"URL":"https:\/\/doi.org\/10.37236\/3532","relation":{},"ISSN":["1077-8926"],"issn-type":[{"type":"electronic","value":"1077-8926"}],"subject":[],"published":{"date-parts":[[2014,12,4]]},"article-number":"P4.49"}}