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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:

  1. 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

neo
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  • What your question is about is unclear. I think i've figured it out, but please confirm: You are having trouble understanding the solution to Warm-Up problem 5, which says "If $a$ and $b$ are positive integers that share no common factor greater than $1$, explain why $ab - a - b$ is always odd.". But I don't understand why you are finding the solution hard to figure out. Could you please be more explicit about where you are confused? – Paul Sinclair Sep 16 '22 at 19:17

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