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Functional equation with squares

Source: Baltic Way 2018, Problem 4

November 6, 2018
algebrafunctional equation

Problem Statement

Find all functions f:[0,∞)→[0,∞)f:[0, \infty) \to [0,\infty), such that for any positive integer nn and and for any non-negative real numbers x1,x2,…,xnx_1,x_2,\dotsc,x_n f(x12+…+xn2)=f(x1)2+⋯+f(xn)2.f(x_1^2+\dotsc+x_n^2)=f(x_1)^2+\dots+f(x_n)^2.
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