Tagged Questions

Questions on more advanced topics of number theory, such as quadratic residues, primitive roots, prime numbers, non-linear Diophantine equations, etc. Consider first if (elementary-number-theory) might be a more appropriate tag before adding this tag.

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Help proving ${n \choose k} \equiv 0 \pmod n$ for all $k$ such that $0<k<n$ iff $n$ is prime.

I can prove the $n$ is prime case: If $n$ is prime, then since $k < n$ and $n$ is prime, the factor of $n$ in the numerator won't be cancelled out. So the question boils down to Let an integer ...
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Representability as a Sum of Three Positive Squares or Non-negative Triangular Numbers

Let $r_{2,3}(n)$ and $r_{t,3}(n)$ denote the number of ways to write $n$ as a sum of three positive squares (A063691) and as a sum of three non-negative triangular numbers (A008443), respectively. I ...
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Suggestion For Books From experts on number theory

Regarding My Background I have covered stuff like 1.Single Variable Calculus 2.Multivariable Calculus (Multiple Integration,Vector Calculus etc) (Thomas Finney) 3.Basic Linear Algebra Course (...
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Bounds for Waring's Problem

The question is posed as such: If G(k) = min{ g : every "sufficiently large" natural number can be written as the sum of g kth powers } Then I seek to prove two things. First, to establish the ...
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Are these two sequences the same?

I was browsing OEIS and came across the largely composite numbers, A067128, defined as the natural numbers that have at least as many divisors as all smaller natural numbers. (They are of course ...