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Results tagged with nt.number-theory
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user 3969
Prime numbers, diophantine equations, diophantine approximations, analytic or algebraic number theory, arithmetic geometry, Galois theory, transcendental number theory, continued fractions
0
votes
General form of amount of triangles that can be formed in an MxN point lattice
ok here is one answer, but I think, you already knew that:
so there are $\left((M+1)(N+1)\atop 3\right)$ possible triangles an we have to subtract the number of triangles, which are degenerated.
Eve …
- 11.1k
4
votes
Accepted
Projective modules over non-rational group rings
I would guess that the map on $K_0$ is an isomorphism, butI could only show the surjectivity right now:
The inclusion of rings $RG\rightarrow QG$ induces a map on $K_0$. Given a projective $RG$-modul …
- 11.1k
4
votes
Pascal triangle and prime numbers
I also wanted to give a very short answer. Let $p$ be a prime number. It is easy to see that the binomial coefficient $\left(p\atop n\right)$ is divisible by $p$ for $1\le n\le p-1$. So the $p$-th lin …
- 11.1k
7
votes
Accepted
A mutation of the Collatz disease
Maybe it is worth to write my comments into an answer:
The question is equivalent to asking whether all elements of the form $n/3^k$ end up in the collatz cycle.
It is still an open question whether …
- 11.1k
2
votes
Lifting matrices mod 2 to integers.
I want to address the weaker question in a more general setting:
Given any matrix over $\mathbb{Z}$ with determinant $1$ mod $m$. Is it possible to add multiples of $m$ to each entry to get a matrix …
- 11.1k
0
votes
Cohomology of $S$-arithmetic groups with trivial coefficients such as $H^n(\rm{PGL}_2(\mathb...
I added this non-answer since it is too long for a comment.
EDIT: In the first version I claimed that the action is free, which it is not.
There is a very explicit model for the classifying space $EPG …