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Results tagged with nt.number-theory
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user 62575
Prime numbers, diophantine equations, diophantine approximations, analytic or algebraic number theory, arithmetic geometry, Galois theory, transcendental number theory, continued fractions
5
votes
1
answer
231
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Can a product of Cohn matrices over the Eisenstein integers with non-zero, non-unit coeffici...
For $k > 1$, is it possible that $\begin{pmatrix} a_1 & 1 \\ -1 & 0 \end{pmatrix}\begin{pmatrix} a_2 & 1 \\ -1 & 0 \end{pmatrix}\ldots \begin{pmatrix} a_k & 1 \\ -1 & 0 \end{pmatrix} = \pm \begin{pmat …
3
votes
Accepted
Can a product of Cohn matrices over the Eisenstein integers with non-zero, non-unit coeffici...
To my surprise, not only is there a solution for some $b$, there is actually a very simple infinite family of solutions for every $b$. Let $\omega = \frac{1 + \sqrt{-3}}{2}$. Then
$\begin{pmatrix} a_0 …