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find n and n nonnegative integers

Source: 11-th Taiwanese Mathematical Olympiad 2002

January 22, 2007

number theory proposednumber theory

Problem Statement

Find all natural numbers

n

and nonnegative integers

x_{1},x_{2},...,x_{n}

such that

\sum_{i=1}^{n}x_{i}^{2}=1+\frac{4}{4n+1}(\sum_{i=1}^{n}x_{i})^{2}