# A Story of an Algorithm

Consider an algorithm for positive integers $n$ and $k$-

Take any multiple of $n$. Multiply the last digit by $k$ and then, add the resulting number to the remaining number to get a number $a$.

For Example- For $n=7$, $k=3$ and multiple of $7=105$, the algorithm would give you $a=10+5×3$.

How many values of $n <1000$ are there such that there exists at least one $k$ for which $a$ is always a multiple of $n$?

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