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Results tagged with nt.number-theory
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user 4760
Prime numbers, diophantine equations, diophantine approximations, analytic or algebraic number theory, arithmetic geometry, Galois theory, transcendental number theory, continued fractions
0
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1
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Can the order of a rational number in Z/pZ be as large as we want
Suppose $d_1, d_2$ are two fixed coprime integers, $\frac{d_1}{d_2} \neq \pm 1$. Given any $n > 0$, can we find a prime number $p$ such that the order of $d_1d^{-1}_2$ in the multiplicative group of t …
4
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2
answers
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Prime ideals in the ring of algebraic integers
Let $m(x) = x^n + a_{n-1}x^{n-1} + \dots + a_1 x+ a_0$, $a_i \in \mathbb{Z}$, be an irreducible polynomial over $\mathbb{Q}$ and $K = \mathbb{Q}[x] / {m(x)\mathbb{Q}[x]}$, so $K$ is an algebraic numbe …
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