Relatively Prime Permutations   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 p2 will not be a permuation of φ(p2).  Problem ID:
240 (10 Aug 2005)     Difficulty: 3 Star  Show Problem &
Solution