# 2012-15 Functional Equation

Let $$n$$ be a fixed positive integer. Find all functions $$f:\mathbb{R}\to\mathbb{R}$$ satisfying $f(x^{n+1}-y^{n+1})=(x-y)[f(x)^n+f(x)^{n-1}f(y)+\cdots+f(x)f(y)^{n-1}+f(y)^n].$

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