# Jan's jazzy sum

Number Theory Level pending

Suppose $$a,b$$ are positive coprime integers such that $\sum_{k = 1}^{b - 1} \left\lfloor \frac{ak}{b} \right\rfloor = 1337.$ If $$S$$ is the sum of all possible values of $$a$$, what are the last three digits of $$S$$?

This problem is posed by Jan J.

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