This is given as the very first part of an explanation to a "Basics" question in Concrete Mathematics - it's not even the answer to the question, just the preamble to the answer. So I'd expect there to be something very obvious about the two operands to mod that I just do not see.
I've seen some variants to the question here and elsewhere, but they too assume that this particular relationship is clear.
Thanks in advance...
(this actually is not my "homework", but I can imagine it is someone's homework - hope it's OK to tag as such)