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Part of 2006 Bosnia and Herzegovina Junior BMO TST

Problems(1)

w = a^{2006} + b^{2006} + c^{2006} + d^{2006}$ is composite when ab = cd

Source: 2006 Bosnia & Herzegovina JBMO TST p3

5/27/2020
Let a,b,c,da, b, c, d be positive integers such that ab=cdab = cd. Prove that w=a2006+b2006+c2006+d2006w = a^{2006} + b^{2006} + c^{2006} + d^{2006} is composite.
number theoryComposite