## Problem #007 - binary multiples

595

Is it true that every integer you can think of has a multiple written out only with $$0$$s and $$1$$s?

### Problem statement

Let $$k \in \mathbb{Z}$$ be an integer. Is there an integer $$n$$ such that $$n$$ is a multiple of $$k$$ and $$n$$ only has $$0$$s and $$1$$s in its decimal expansion?

As an example, if $$k = 2$$ we could have $$n = 10$$.

If you need any clarification whatsoever, feel free to ask in the comment section below.

### Solution

You can read the solution here to compare with your own solution.