From Pinter 'A Book on Abstract Algebra' 2nd Ed.

Question E-2 from Ch. 10 on page 109

Let a and b be elements of a group G. Let ord(a)=m and ord(b)=n; let lcm(m,n) denote least common multiple of m and n. Prove if m and n are relatively prime, then no power of a can be equal to any power of b (except for e(the identity)).

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