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f(2) = 7, find all integer functions [Taiwan 2014 Quizzes]

Source:

July 18, 2014
functionlogarithmsintegrationTaiwan

Problem Statement

Find all increasing functions ff from the nonnegative integers to the integers satisfying f(2)=7f(2)=7 and f(mn)=f(m)+f(n)+f(m)f(n) f(mn) = f(m) + f(n) + f(m)f(n) for all nonnegative integers mm and nn.
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