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On distinct residues of factorials. (English) Zbl 1432.11016

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 \(10^{11}\).

MSC:

11B65 Binomial coefficients; factorials; \(q\)-identities
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