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# Fun with factorials

Find all natural numbers $$n$$ such that $$n! | a^n+1$$ for all $$0$$ <$$a \le n!$$ with natural number $$a$$.

Note by Surya Prakash Bugatha
2 years, 7 months ago

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Ehh, $$2^n+1$$ is less than $$n!$$ for $$n<4$$, so you got only 3 cases to check...

- 2 years, 7 months ago

Hint: What happens when $$a = 0$$?

Staff - 2 years, 7 months ago

Ooops!! Typo fixed

- 2 years, 7 months ago

Hint: What happens when $$a = 1$$? What happens when $$a = n$$?

Staff - 2 years, 7 months ago