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NMC 2011 Problem 3

  • Answer

Find all functions ff such that

f(f(x)+y)=f(x2−y)+4yf(x)f(f(x)+y)=f\left(x^{2}-y\right)+4 y f(x)

for all real numbers xx and yy.

Dataset text NuminaMath olympiads. Quoted with source.

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f(x)=0 \text{ or } f(x)=x^2

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