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f(2) = a > 2, f(mn) = f(m)f(n), increasing, minimum a

Source: Nordic Mathematical Contest 1987 #3

October 5, 2017

minimum valueincreasing functionsfunctional equation in Nalgebra

Problem Statement

Let

f

be a strictly increasing function defined in the set of natural numbers satisfying the conditions

f(2) = a > 2

and

f(mn) = f(m)f(n)

for all natural numbers

m

and

n

. Determine the smallest possible value of

a