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Results tagged with nt.number-theory
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user 468
Prime numbers, diophantine equations, diophantine approximations, analytic or algebraic number theory, arithmetic geometry, Galois theory, transcendental number theory, continued fractions
55
votes
Accepted
On the series 1/2 + 1/3 + 1/5 + 1/7 + 1/11 + ...
Yes, it's possible. Define the closed sets to be the sets the sum of whose reciprocals converges, together with $\mathbb{N}$. This collection of subsets is closed under arbitrary intersection and fi …
- 6,302
7
votes
Finitely many arithmetic progressions
This is "the same" as the generating function proof, but it doesn't use generating functions explicitly. Take the largest common difference in any of the sequences, say n, and pick $\zeta$ a primitiv …
- 6,302
1
vote
What can be said about number-theoretic properties of the solid angle measures of polytopal ...
$S_n$ acts on the set of cones, and preserves the solid angle measure. If you consider the $n!$ rotations of the cone by elements of $S_n$, and except on the union of some hyperplanes, the number of …
- 6,302
5
votes
Accepted
Counting lattice points inside a parallelepiped
I have not filled in absolutely all the details, but hopefully this is enough to be convincing.
Let's let $M$ take positive integer values, and let's consider the parallelepiped: $$P'=\{x+Mtv\mid x\in …
- 6,302