nprofile1qyt8wumn8ghj7un9d3shjtnyd968gmewwp6kytcqyrt40hcuxctvenkxq2rzwpj004jjmx6fphfx9hn3meahe2kccu7fxmxaamk (nprofile…aamk) I'm ashamed to admit it, but:
It holds in an arbitrary commutative ring (no assumptions like being a domain) that if a and b are not units then ab is not a unit.
(After I did the proof, I concluded that this was the right time to stop my work day.)