olymmath

TW-TST 2002 Problem 1

    Find all natural numbers nn and nonnegative integers x1,x2,...,xnx_{1},x_{2},...,x_{n} such that ∑i=1nxi2=1+44n+1(∑i=1nxi)2\sum_{i=1}^{n}x_{i}^{2}=1+\frac{4}{4n+1}(\sum_{i=1}^{n}x_{i})^{2} .

    Dataset text AI-MO AoPS. Quoted with source.

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