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xf(y)+yf(x)=(x+y)f(x)f(y) - ILL BUL2

Source: ILL BUL2

September 29, 2010
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Problem Statement

Find all functions ff defined for all xx that satisfy the condition xf(y)+yf(x)=(x+y)f(x)f(y),xf(y) + yf(x) = (x + y)f(x)f(y), for all xx and y.y. Prove that exactly two of them are continuous.
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