Question

suppose \(n\mid (a^n-a)\) for all \(a\) and \(n\) is the least such positive power of \(a\).

show that \(n\) is prime

Answer 1

\(\Large n|a(a^{n-1}-1)\)
so n|a
or \(\Large n|{a^{n-1}-1}\)
first one
when n is prime
a^n=a mod n
huh lol xD i'll complete ltr

Answer 2

didnt reemove my comment so i would remember when i come back!