This is a followup question to Appropriate Reaction to a Failed Reference Request on MO related to Reference Request for Integer factorization with LP/ILP

I'm about to prepare an answer that contains my way of formulating integer factorization as an optimization problem that can be solved with the integer variant of the simplex method.

Now I have the options of either presenting the answer with just enough detail to understand it and judge its correctness and/or its practical relevance, or I could also supply some background information, that would have a more "entertaining" quality, e.g. what was the original motivation, difficulties encountered, etc.
The background information could of course be supplied well separated from the "technical" part.

I would like to get some opinions on the usefulness and desirability of documenting such background information.
Also replies related to other mathematical results, for which background information is available or not, are welcome.