I read the term “number theory” for the first time in 2010, in this book (for RMO preparation):
This term didn’t make any sense to me then. More confusing was the entry in footer “Number of Theory”. At that time I didn’t have much access to internet to clarify the term, hence never read this chapter. I still like the term “arithmetic” rather than “number theory” (though both mean the same).
Yesterday, following article in newspaper caught my attention:
The usage of this term makes sense here!