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Problem

Euler's Totient function, φ($n$), is used to determine the number of numbers less than $n$ that are relatively prime to $n$. For example, φ(6) = 2, because only 1 and 5 are relatively prime with 6.

Interestingly, φ(63) = 36, and this is the first example of a number which produces a permutation of the value of its Totient function.

Given that $p$ is prime, prove that $p$ will not be a permutation of φ($p$), and prove that $p$² will not be a permuation of φ($p$²).