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OlympiadSuperchallengeOlympiad Number Theory

Olympiad Number Theory · Superchallenge problem

A function f:R→Rf:\mathbb R\to\mathbb R satisfies f(x)f(y)−f(xy)=x+yf(x)f(y) - f(xy) = x + y for all real x,yx, y. Compute f(5)f(5).