Hint to puzzle 128: Modular equation

Firstly, note that, for relatively prime integers m and n, x⁴⁹ x (modulo mn) x⁴⁹ x (modulo m) and x⁴⁹ x (modulo n).

Next, by considering x⁴⁹ x (modulo p^r), where p is prime, r 1, and x = p^r−1, show that r > 1 is impossible.