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Results tagged with nt.number-theory
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user 160051
Prime numbers, diophantine equations, diophantine approximations, analytic or algebraic number theory, arithmetic geometry, Galois theory, transcendental number theory, continued fractions
6
votes
What are the best known bounds for the smallest primes larger than $n$?
I will write here an approach which gives some interesting upper bounds on $p$ and $q$. The trivial lower bounds are $p \geq n$ and $q \geq p (\geq n)$. The idea shown here does not give an effective …
- 1,175
3
votes
Accepted
Irrationality measure of powers
Let $\alpha$ be irrational. There are two cases: $\alpha$ can be either algebraic or transcendental. Products of algebraic numbers are algebraic, while rational powers of transcendental numbers are tr …
- 1,175