Question: Given an integral domain (D, +, ) with zero element z, let a, b D with ab z. (a) If a3 = b3

Given an integral domain (D, +, •) with zero element z, let a, b ∈ D with ab ≠ z. (a) If a3 = b3 and a5 = b5, prove that a = b. (b) Let m, n ∈ Z+ with gcd(m, n) = 1. If am = bm and an = bn, prove that a = b.

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a Since a 3 b 3 and a 5 b 5 it follows that a 5 b 3 b 2 a 3 b 2 Consequen... View full answer

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