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f(x + y) + f(x − y) = 2f(x) + 2f(y) in Q

Source: Nordic Mathematical Contest 1998 #1

October 3, 2017
functional equationrational functionfunctionalgebra

Problem Statement

Determine all functions f f defined in the set of rational numbers and taking their values in the same set such that the equation f(x+y)+f(xāˆ’y)=2f(x)+2f(y) f(x + y) + f(x - y) = 2f(x) + 2f(y) holds for all rational numbers xx and yy.
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