I try to get a feeling for the role modular arithmetic does play in (elementary) number theory.
See the comment on the importance of modularity in Iwaniec & Kowalski 2004, p. 1
Modular arithmetic might be described as the study of divisibility relations between integer numbers in the form of equations. I assume this is a main part of elementary number theory. But if it's not all that is elementary number theory about, what else?
Finally: Where outside of number theory does modular arithmetic play a role? Or only as a part of number theory? Possibly in a field like arithmetic geometry?