# Finding valid keys in a cryptosystem (m^k + mod 41)

I'm studying for an exam I have tomorrow and could not find the answer to the following question:

For which of the following values of k is $$E_{k}(m) = m^{k} mod 41$$ a cipher over $$Z_{41}$$ ?

And the possible values of k is: 3, 5, 7

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If by a cipher you mean a bijection, then both $k=3$ and $k=7$ work because they are prime with $40=\phi(41)$, but $k=5$ isn't.