So I was looking at a few strong induction problems such as the following "Given an unlimited supply of 5 cent and 7 cent stamps, what postages are possible?" and it seems the computation for base case scenarios is done manually but I wanted to explore a standardised way of working with such problems, and so I came across the following link http://math.bu.edu/people/freer/root/mathprojects/postage/links/postage_lnk_8.asp
I'll reference the part I'm interested in below, but I'm having a hard time understanding how they got to the ab-a-b formula, I've checked it against a few problems I'm working with and it seems to work as a generalised way of going about these problems
Here's the main part I referenced earlier:
- We can't have two even values for a and b, so either both are odd; or one is odd and the other is even.
If both are odd, a times b minus a minus b is odd when both a and b are odd
If one is even -- assume it's a, a times b minus a minus b is odd when a is even and b is odd