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Hint to puzzle 128: Modular equation

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

Next, by considering x49 congruent to x (modulo pr), where p is prime, r greater than or equal to 1, and x = pr−1, show that r > 1 is impossible.