"The word `basic’ in the title is closer in meaning to `foundational’ rather than `elementary’ [...]" (quoted from that same wikipedia page).
"The title is the same as that of a very well-known book by Professor
L. E. Dickson (with which ours has little in common). We proposed
at one time to change it to 'An introduction to arithmetic', a more novel
and in some ways a more appropriate title; but it was pointed out that
this might lead to misunderstandings about the content of the book."
G.H. Hardy and E. M. Wright "An Introduction to the Theory of Numbers"
The one math majors joke about is Serra’s A Course in Arithmetic, which is definitely not for young children.
I remember a joke along the lines of "elementary" meaning that someone somewhere has solved it before.
"Any question in maths is either unsolved or obvious."