# 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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### is all math beyond arithmetic just advanced arithmetic? [on hold]

Is it true that at the bare-bones of all advanced math, its all just mostly arithmetic? In computer programming languages they are mostly constrained to arithmetic operators. I suppose this is ...
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### New Generalized MR-test

I am conducting a new Miller Rabin (SPRP test) and editing the first step. Can someone please help me with the last step. Thanks. Original: Write $n$ $=$ $2^sd+1$ with $d$ odd. Replace: New Test: ...
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### Topics on Number theory for undergraduate to do a project [closed]

Im an undergraduate in the mathematics field ..So i wanna be alittle more productive and wanted to do an essay or project mostly on number theory or Algebra(Rings or Groups) and i want to ask if you ...
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### Can we find exact factor of inert prime ideals?

$K=\mathbb{Z}[\sqrt{m}]$ with $m$ being square free. I studied the proof of the statement that a prime ideal $\mathfrak{p}=\langle p \rangle$ of $\mathbb{Z}$ stays inert in $\mathcal{O}_K$ if $p=2$...
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### The Spacing of $e$ and $\pi$ Segments Within the Decimal Expansion of $\pi$

I discovered something seemingly very improbable today when I was searching for segments of $e$ and $\pi$ within the decimal expansion of $\pi$. I searched for $314159265$ and found it starts at the ...
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### Do these series converge to the von Mangoldt function?

Jeffrey Shallit formulated this recurrence for me: $\displaystyle T(n,1)=1, k>1: T(n,k) = \sum\limits_{i=1}^{k-1} T(n-i,k-1)-\sum\limits_{i=1}^{k-1} T(n-i,k)$ which is the lower triangular array ...
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### little Fermat theorem generalization proof without Burnside's lemma

Burnside's Lemma Deduce That: $$\sum_{i=1}^n a^{gcd(i,n)}$$ is divisible by $n$ it's a beautiful result. but i want to prove it without any abstract algebraic tools such as Burnside's Lemma... is ...
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### Game of replacing number with divisors

In a game , there are N numbers and 2 player(A and B) . ...
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### Any Mersenne prime contains two consecutive 9 digits? [on hold]

The kids with me were each asked to pick a number. It crossed my mind that a smart aleck might answer with a description of some number that we have never actually computed. I remembered that a ...