July 11th, 2019, 04:48 AM  #1 
Member Joined: Apr 2011 Posts: 36 Thanks: 0  Why these topics?
Why are gcd, Diophantine equations, primes, Fundamental Theorem of Arithmetic, modular arithmetic, Fermat's Little Theorem, Euler's Theorem, primitive roots, quadratic residues, Pythagorean triples and so on fundamental in an elementary number theory course? Every elementary number theory course has these topics. 
July 11th, 2019, 04:56 AM  #2 
Senior Member Joined: Oct 2009 Posts: 863 Thanks: 328 
Why not? Why does every analysis course have continuity, integration, differentiability? Why not? I'm really unsure what kind of answer you expect here. 

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elementary number theory, philosophical, teaching, topics 
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