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- Thread starter matqkks
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In summary, elementary number theory courses cover topics such as 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 because they are necessary tools for understanding and working with number theory. Without these foundations, it would be difficult to delve into more complex concepts such as the Riemann Hypothesis or the prime number theorem. Additionally, many conjectures in number theory appear simple on the surface but are actually incredibly difficult to prove analytically, making the subject an "analytical nightmare."

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Mentor

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Diophantine equations can be devilishly hard to solve analytically.

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$$\text{ There is always a prime between }n^2 \text{ and }(n+1)^2$$

I mean, could it look more innocent?

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That’s a nice conjecture that I’ve not heard of before either.

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http://garden.irmacs.sfu.ca/

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