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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 $N:1$, …
Allan MacLeod's user avatar
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 …
Allan MacLeod's user avatar