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Results tagged with nt.number-theory
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user 35673
Prime numbers, diophantine equations, diophantine approximations, analytic or algebraic number theory, arithmetic geometry, Galois theory, transcendental number theory, continued fractions
5
votes
Does there exist a non-square number which is the quadratic residue of every prime?
Let $a$ be any non-square. Then write $a=p^nm$ for some odd $n$ and prime $p$ which does not divide $m$. By Dirichlet's Theorem on primes in arithmetic progressions and the Chinese Remainder Theorem w …
- 133
1
vote
When does a Bohr set have the right size?
To some extent one can obtain upper bounds on $B(\Gamma,\epsilon)$ when $\Gamma$ is quite special. For instance, when $\Gamma$ is dissociated (which is to say, the sums $\sum_{s\in S}s$ are distinct f …
- 133
3
votes
1
answer
376
views
When does a Bohr set have the right size?
Fix a set $
\Gamma\subset \mathbb F_p$, the field with $p$ elements and a parameter $\epsilon>0$. The Bohr set $B(\Gamma,\epsilon)$ consists of those $x$ for which $x\cdot \Gamma\subseteq[-\epsilon p, …
- 133