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

Source: 2006 Bosnia & Herzegovina JBMO TST p3

May 27, 2020
number theoryComposite

Problem Statement

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.
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