Question
Let $p$ be a prime and $k$ a positive integer such that $a^{\mathrm{k}}$ mod $p=$ $a \bmod p$ for all integers $a$. Prove that $p-1$ divides $k-1$.
Step 1
We have $1^k \equiv 1 \pmod{p}$, which is true for all primes $p$ and all positive integers $k$. Show more…
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