Monday, 3 July 2017

Functional equation (show that)

Show that there does not exist a function $f:\mathbb N\to \mathbb N$ which satisfy
a) $f(2) = 3$
b) $f(mn) = f(m)\cdot f(n)$ for all $m,n \in \mathbb N$
c) $f(m) < f(n)$ whenever $m < n$

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