MHB Why certain topics in elementary number theory?

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Elementary number theory courses focus on foundational topics such as gcd, linear Diophantine equations, and the Fundamental Theorem of Arithmetic because these concepts represent the core problems in the field. The inclusion of modular arithmetic, Fermat's Little Theorem, and Euler's Theorem further emphasizes the essential principles that underpin number theory. Discussions highlight a common misconception where elementary number theory is confused with basic arithmetic or elementary math. Understanding these topics is crucial for grasping more complex number theory concepts. The curriculum is designed to build a strong mathematical foundation for students.
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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?
 
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?? Because those are the most basic problems in number theory!
 
He probably confused elementary number theory with elementary number problem, in other words, elementary math.
 

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