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At least one of b^2+b+1 and c^2+c+1 is composite.

Source: 2019 Baltic Way P18

November 18, 2019
number theory

Problem Statement

Let a,ba,b, and cc be odd positive integers such that aa is not a perfect square and a2+a+1=3(b2+b+1)(c2+c+1).a^2+a+1 = 3(b^2+b+1)(c^2+c+1). Prove that at least one of the numbers b2+b+1b^2+b+1 and c2+c+1c^2+c+1 is composite.
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