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Results tagged with nt.number-theory
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user 9003
Prime numbers, diophantine equations, diophantine approximations, analytic or algebraic number theory, arithmetic geometry, Galois theory, transcendental number theory, continued fractions
1
vote
Orbits in modular arithmetic
Thanks to Gjergji's post and subsequent comment, I was able to arrive at his answer after some effort. I post the full proof here for anyone who might find it useful.
Let $p \ge 5$ be a prime number …
- 133
9
votes
3
answers
2k
views
Orbits in modular arithmetic
Let $p$ be an odd prime number and consider the set of $p-2$ integers that is $\mathbb{Z}_p$ minus 0 and 1. Next define two bijective functions on this set
\begin{align}
f(x) &= 1-x \mod p
\end{align} …
- 133
2
votes
0
answers
682
views
Strong Bezout's Identity?
Let $\{ a_i \}_{i=1}^N $ be a set of elements of the ring of integers, $\mathbb{Z}_D$ and define $g = \text{gcd}(a_1, a_2,\ldots, a_N, D)$. Then Bezout's Identity states that there exists another set …
- 133