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Posted: **Mon Jul 11, 2022 12:01 pm**

: Let R Be A Unique Factorisation Domain Let A And B Be Two Elements Of R With Gcd A B 1 Suppose That There Exists X 1 (43.92 KiB) Viewed 28 times

Let R be a unique factorisation domain. Let a and b be two elements of R with gcd(a, b) = 1. Suppose that there exists x ER with ab = x². Prove that there exists u, v, y, z E R with u and v units such that a = uy² and b = vz².