Nuno Freitas

activity

20112026

most citedThe Asymptotic Fermat's Last Theorem for Five-Sixths of Real Quadratic Fields

41 citations · 104 across the 25 of their papers we have counts for

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Showing 2016Show all

4 papers · 1 filter

math.NT2016★ 1 cited

On the symplectic type of isomorphims of the p-torsion of elliptic curves

Nuno Freitas, Alain Kraus

Let $p \geq 3$ be a prime. Let $E / Q$ and $E^{'} / Q$ be elliptic curves with isomorphic $p$ -torsion modules $E [p]$ and $E^{'} [p]$ . Assume further that either (i) every $G…

math.NT2016

An application of the symplectic argument to some Fermat-type Equations

Nuno Freitas, Alain Kraus

Let $p$ be a prime number. In the early 2000s, it was proved that the Fermat equations with coefficients \[3x^p + 8y^p + 21z^p =0\quad \text{ and } \quad 3x^p + 4y^p + 5z^p=0 \] do…

math.NT2016

A result on the equation $x^{p} + y^{p} = z^{r}$ using Frey abelian varieties

Nicolas Billerey, Imin Chen, Luis Dieulefait +1

We prove a diophantine result on generalized Fermat equations of the form $x^{p} + y^{p} = z^{r}$ which for the first time requires the use of Frey abelian varieties of dimension $\geq 2…

math.NT2016

On the Fermat-type Equation $x^{3} + y^{3} = z^{p}$

Nuno Freitas

We prove that the Fermat-type equation $x^{3} + y^{3} = z^{p}$ has no solutions $(a, b, c)$ satisfying $ab c \neq = 0$ and $g cd (a, b, c) = 1$ when $- 3$ is not a square mod~ $p$ . This improves to a…

On the symplectic type of isomorphims of the p-torsion of elliptic curves

An application of the symplectic argument to some Fermat-type Equations

A result on the equation xp+yp=zr using Frey abelian varieties

On the Fermat-type Equation x3+y3=zp

A result on the equation $x^{p} + y^{p} = z^{r}$ using Frey abelian varieties

On the Fermat-type Equation $x^{3} + y^{3} = z^{p}$