Mock AIME 1 2006-2007 Problems/Problem 12

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12. Let $k$ be a positive integer with a first digit four such that after removing the first digit, you get another positive integer, $m$, that satisfies $14m+1=k$. Find the number of possible values of $m$ between $0$ and $10^{2007}$.

Mock AIME 1 2006-2007