Andrejić, Vladica; Tatarević, Miloš On distinct residues of factorials. (English) Zbl 1432.11016 Publ. Inst. Math., Nouv. Sér. 100(114), 101-106 (2016). Summary: We investigate the existence of primes \(p > 5\) for which the residues of \(2!, 3!, \ldots, (p-1)!\) modulo \(p\) are all distinct. We describe the connection between this problem and Kurepa’s left factorial function, and report that there are no such primes less than \(10^{11}\). Cited in 3 Documents MSC: 11B65 Binomial coefficients; factorials; \(q\)-identities Keywords:left factorial; factorial; prime numbers PDFBibTeX XMLCite \textit{V. Andrejić} and \textit{M. Tatarević}, Publ. Inst. Math., Nouv. Sér. 100(114), 101--106 (2016; Zbl 1432.11016) Full Text: DOI arXiv