An algebra problem by Priyanshu Mishra

Algebra Level 3

Let f f be a one-to-one function from the set of natural numbers to itself such that f ( m n ) = f ( m ) f ( n ) f(mn) =f(m)f(n) for all natural numbers m m and n n . What is the least possible value of f ( 999 ) f(999) ?


The answer is 24.

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