BALKAN-SL 2014 N5

$\boxed{N5}$ Let $a,b,c,p,q,r$ be positive integers such that $a^p+b^q+c^r=a^q+b^r+c^p=a^r+b^p+c^q.$ Prove that $a=b=c$ or $p=q=r.$

Dataset text AI-MO AoPS. Quoted with source.

Solutions

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