Why elementary number theory includes gcd through quadratic residues

[matqkks]

Why do all elementary number theory courses have the following topics - gcd, linear Diophantine equations, Fundamental Theorem of Arithmetic, factorization, modular arithmetic, Fermat's Little Theorem, Euler's Theorem, primitive roots, quadratic residues and nonlinear Diophantine equations?

 

[HallsofIvy]

?? Because those are the most basic problems in number theory!

 

[Monoxdifly]

He probably confused elementary number theory with elementary number problem, in other words, elementary math.