Last night, I was exploring the Internet, when I stumbled across a very cool diagram. It look like this:
With this graph, you can see what numbers are divisible by 7. Lets take the number 1234567. You would first start at the white node at the bottom. First move 1 black arrow, then 1 white arrow, then 2 black arrows, then 1 white arrow, then 3 black arrows, the 1 white arrows, and so on and so forth. For each digit number of black arrows you move, you move 1 white arrow. If you end up at the start, then it is divisible by 7. However number of black arrows away from the start you are is the remainder. Can someone prove this?