olymmath

NMC 2008 Problem 1

  • Answer

Determine all real numbers A,BA, B and CC such that there exists a real function ff that satisfies

f(x+f(y))=Ax+By+Cf(x+f(y))=A x+B y+C

for all real xx and yy.

Dataset text NuminaMath olympiads. Quoted with source.

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(A, B, C) = (a, a^2, c) \text{ where } a \neq -1 \text{ and } c \text{ are arbitrary, or } (A, B, C) = (-1, 1, 0)

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