Erdős Problem #478 — Let $p$ be a prime and $A_p = \{ k! \pmod{p} : 1\leq k<p\}.$ Is it true that $\lvert A_p\rvert \sim (1-\tfrac{1}{e})p?$

About 46 years old · traced to 1980

Let $p$ be a prime and $A_p = \{ k! \pmod{p} : 1\leq k<p\}.$ Is it true that $\lvert A_p\rvert \sim (1-\tfrac{1}{e})p?$

References

Primary source

ULAM AI, UnsolvedMath dataset, Erdős Problems set, revision b9437975f3c873f635a13c48f8b022f5ba80898a; CC BY 4.0.

Additional references

UnsolvedMath, Erdős Problems set, ULAM AI, licensed CC BY 4.0.

factorials number-theory

InErdős Problems

Posted 1 month ago · edited 3 weeks ago

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