# Divide and conquer

Let $$\overline{ABC}$$ be a three digit positive integer with $$A>C \ge 0$$ and having the property that

$$\overline{ABC} \equiv 0 \mod \overline{CBA}$$.

If $$n_1,n_2,\cdots,n_k$$ are $$k$$ numbers satisfying the above constraints,

Find $$n_1+n_2+\cdots+n_k$$

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