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On the value set of \(n!\) modulo a prime. (English) Zbl 1161.11386

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 \(n\).

MSC:

11N69 Distribution of integers in special residue classes
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