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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
1 year, 11 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... · 1 year, 11 months ago

Hint: What happens when $$a = 0$$? Staff · 1 year, 11 months ago

Ooops!! Typo fixed · 1 year, 11 months ago

Hint: What happens when $$a = 1$$? What happens when $$a = n$$? Staff · 1 year, 11 months ago