I attached my question as a file, hope you don't mind, i do not fully understand how i'm supposed to work this one out. Thank you in advance.

Irreducible: An element p ∈ R is irreducible if

UFD: Unique factorisation domain

Given that R is an UFD

Proof that given that n > 1 en a1,a2,b ∈ R\R* with b^n = a1a2 such that a1 and a2 have no common irreducible factors; than there exist b1,b2 ∈ R \ R* and u1,u2 ∈ R* such that