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(a + b + c) | (a - b)^2 + (b - c)^2 + (c - a)^2

Source: Czech-Polish-Slovak Junior Match 2018, Team p1 CPSJ

March 7, 2020
number theorydividesdivisible

Problem Statement

For natural numbers a,bca, b c it holds that (a+b+c)2∣ab(a+b)+bc(b+c)+ca(c+a)+3abc(a + b + c)^2 | ab (a + b) + bc (b + c) + ca(c + a) + 3abc. Prove that (a+b+c)∣(a−b)2+(b−c)2+(c−a)2(a + b + c) |(a - b)^2 + (b - c)^2 + (c - a)^2
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