Baltic Way 2019 · Problem 18

Number Theory

Let $a,b,c$ be odd positive integers such that $a$ is not a perfect square and

a^2+a+1=3(b^2+b+1)(c^2+c+1).

Prove that at least one of the numbers $b^2+b+1$ and $c^2+c+1$ is composite.

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Review

Diophantine equations

No verified local solution is currently available.

Results from Baltic Way 2019

11 teams

Score distribution

All team scores