Show that there exits infinitely many functions $f:\mathbb{N}\to\mathbb{N}$ satisfying
(a) $f(2)=4;$
(b) $f(mn)=f(m)f(n)$ for every $m,n\in\mathbb{N};$
(c) $f(m)<f(n)$ whenever $m<n.$
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3What have you tried? (b) should remind you of prime factorization. – Ross Millikan Jan 23 '20 at 02:55
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$f(x)=x^2$ is actually the only solution. – user574848 Jan 24 '20 at 09:08