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Results tagged with nt.number-theory
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user 24864
Prime numbers, diophantine equations, diophantine approximations, analytic or algebraic number theory, arithmetic geometry, Galois theory, transcendental number theory, continued fractions
8
votes
1
answer
420
views
Probability in the Primes
Given two randomly chosen positive rational integers, the probability that the two numbers are coprime is $\frac{6}{\pi^2}$. This is also the probability that a positive integer is squarefree. Are the …
- 801
4
votes
2
answers
804
views
Factor rings of the ring of integers in a number field
The factor rings of the ordinary integers $\mathbb Z$ are the well-known residual classes $\mathbb Z_n$. For the Gaussian integers $\mathbb Z[i]$ the factor rings are studied in
1) J. T. Cross, The …
- 801
4
votes
0
answers
201
views
Primes in integral domains
Let $\mathcal O_{\mathbb K}$ be the ring of integers in a number field $\mathbb K$. It is easy to prove that the number of (non-associated) primes in $\mathcal O_{\mathbb K}$ is infinite.
On the other …
- 801
7
votes
1
answer
1k
views
Menon’s identity
I also put this question in stackexchange, but remained unanswered. https://math.stackexchange.com/questions/506996/menons-identity
Let $G$ be a group of order $n$. Consider an action of $U_n$, the g …
- 801