Divibility of a polynomial over the integers.
I've been working through some number theory problems lately. One of them stumped me for a bit on polynomials over the integers and I ended up taking it to math.stackexchange.com. Turns out these polynomials have been used in something called turbo coding" too. Surprisingly, if you have a 4G phone you've probably already got these polynomials in your pocket in the form of a bit interleaver which is keeping your phone call clear and noise free.