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RU-ALLRUSSIAN 1962 Problem 12

  • Answer

Given unequal integers x, y, z prove that (x−y)5+(y−z)5+(z−x)5\left(\mathrm{x - y}\right)^{5} + \left(\mathrm{y - z}\right)^{5} + \left(\mathrm{z - x}\right)^{5} is divisible by 5(x−y)(y−z)(z−x)5(\mathrm{x - y})(\mathrm{y - z})(\mathrm{z - x}) .

Dataset text NuminaMath olympiads. Quoted with source.

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  • 5\mathrm{rs}(\mathrm{r + s})(\mathrm{r}^{2} + \mathrm{rs} + \mathrm{s}^{2})

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