Math Team Challenge

Here's a problem that the Gateway math team will be tackling soon. Would you have any idea how to go about this?

You have a board with checkers set up in the standard configuration (i.e. the black squares on the first three rows and the last three rows have pieces on them, while all the others do not). You can make a piece jump over one that's diagonally adjacent to it and remove the piece that was jumped over.

After doing this repeatedly, can you end up with just one piece in the bottom left square?

Hint: This has something to do with what is called modulo (or modular) arithmetic, which the math team has been learning about recently. This is a tool used in number theory, which is a major topic in college-level math.