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Results tagged with nt.number-theory
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user 88700
Prime numbers, diophantine equations, diophantine approximations, analytic or algebraic number theory, arithmetic geometry, Galois theory, transcendental number theory, continued fractions
10
votes
Polynomial bijection from ZxZ to Z?
It is an open problem. Maximal results about bijections from
$\mathbb N\times \mathbb N$, $\mathbb Z\times \mathbb N$, $\mathbb Z\times \mathbb Z$ to $\mathbb N$ are contained in
John S. Lew, Arn …
- 286
1
vote
How many ways can one cover $\mathbb Q_p$ with the images of polynomials?
In your example covering is an almost partition (the only common point is $0$). If you allow overlapping, covers can be rather complicated. For exmaple, in $\mathbb Q_5$:
$$
x^2, \ 2x^2, \ x^3, \ 5x^6 …
- 286
6
votes
Accepted
What polynomials biject from $\mathbb{N}^{2}$ to $\mathbb{N}$?
Describing such bijections is an open problem. Maximal result (there is no other bijections among polynomials of degree not higher than 4) are contained in
John S. Lew, Arnold L. Rosenberg,
Poly …
- 286