## 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