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Prime numbers, diophantine equations, diophantine approximations, analytic or algebraic number theory, arithmetic geometry, Galois theory, transcendental number theory, continued fractions
5
votes
Diophantine equation $2(x - 1/x) = y - 1/y$
This question is actually the first example, in a different formulation, of the following problem:
Find two integer right-angled triangles with a common base and altitudes in the integer ratio $N:1$, …
9
votes
1
answer
810
views
Parametric families for large torsion subgroups of elliptic curves
The following are two facts about $\mathbb{Z}/9\mathbb{Z}$, $\mathbb{Z}/10\mathbb{Z}$, $\mathbb{Z}/12\mathbb{Z}$,
$\mathbb{Z}/2\mathbb{Z} \times \mathbb{Z}/8\mathbb{Z}$.
(a) According to Andrej Duje …