I'm having difficulty making progress on the following proof, and I'm hoping for some hints to help me along.
Let denote a fixed positive integer. Prove the following statement by induction: For every integer , there exist non-negative integers and such that
So I can state the assertion and show the initial case is true:
I've tried picking a value for b and creating a table of related values for q and r as n counts up from 0. But I can't figure out how to express the patterns I see to form a usable general case and inductive step.
Again, just looking for hints right now to help get me out of the rut I'm in.