Positive integers $a < b < c$ are such that $b + a$ is a multiple of $b - a$ and $c + b$ is a multiple of $c-b$. If $a$ is a $2011$-digit number and $b$ is a $2012$-digit number, exactly how many digits does $c$ have?
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Tags: Digits, number theory
Positive integers $a < b < c$ are such that $b + a$ is a multiple of $b - a$ and $c + b$ is a multiple of $c-b$. If $a$ is a $2011$-digit number and $b$ is a $2012$-digit number, exactly how many digits does $c$ have?