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MathNet 1985 — Part 01 Question 25

Math Olympiad Vault · MathNet 1985 — Part 01

Question 25

The function $f(n)$ is defined on the positive integers and takes non-negative integer values. It satisfies

(1) $f(m n) = f(m) + f(n)$,

(2) $f(n) = 0$ if the last digit of $n$ is $3$,

(3) $f(10) = 0$.

Find $f(1985)$.