On the Value Set of n! Modulo a Prime

Authors: WILLIAM D. BANKS, FLORIAN LUCA, IGOR E. SHPARLINSKI, HENNING STICHTENOTH

Abstract: 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.

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