One context in which diophantine equations arise is hidden within the innards of loop optimizing compilers, where loop carried dependencies are considered, as they constrain parallelization.

I had (and donated to an engineering library in Urbana) a book about just this from the early 90s. I tried finding it on Amazon but no such luck.

This was a recurrent tool at

https://en.wikipedia.org/wiki/University_of_Illinois_Center_...