CZ-SK-MO 2015 Problem 4

Find all real triples $(a,b,c)$ , for which $a(b^2+c)=c(c+ab)$ $b(c^2+a)=a(a+bc)$ $c(a^2+b)=b(b+ca).$

Dataset text AI-MO AoPS. Quoted with source.

Solutions

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