1985 OIM Problems/Problem 5

Problem

To each positive integer $n$ we assign an integer non-negative $f(n)$ such that these conditions are satisfied:

(i) $f(rs)=f(r)+f(s)$

(ii) $f(n)=0$ , when the unit digit of $n$ is 3

(iii) $f(10)=0$

Find $f(1985)$ . Justify your answer.

~translated into English by Tomas Diaz. ~orders@tomasdiaz.com

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