Banks, William D.; Luca, Florian; Shparlinski, Igor E.; Stichtenoth, Henning On the value set of \(n!\) modulo a prime. (English) Zbl 1161.11386 Turk. J. Math. 29, No. 2, 169-174 (2005). Summary: We show that for infinitely many prime numbers \(p\) there are at least \(\log \log p/\log \log \log p\) distinct residue classes modulo \(p\) that are not congruent to \(n!\) for any integer \(n\). Cited in 7 Documents MSC: 11N69 Distribution of integers in special residue classes PDF BibTeX XML Cite \textit{W. D. Banks} et al., Turk. J. Math. 29, No. 2, 169--174 (2005; Zbl 1161.11386) Online Encyclopedia of Integer Sequences: Irregular triangle: T(n, k) = k! modulo prime(n), 1<k<prime(n), 1<n. Number of permutations in S_n that are factorials of permutations in lexicographic order.