Minimum Powers

Level pending

Let set $$S$$ be the set of integers that can be expressed in the form $$2^m+3^n$$, for nonnegative integers $$m, n$$. Let $$m$$ be the minimum of $$|100000-a|$$, where $$a$$ is an element in $$S$$. Find the last 3 digits of $$m$$

×