3

Part of 1987 Nordic

Problems(1)

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

Source: Nordic Mathematical Contest 1987 #3

f

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

f(2) = a > 2

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

for all natural numbers

m

n

. Determine the smallest possible value of

a

minimum valueincreasing functionsfunctional equation in Nalgebra