Alejandro Arg'aez-Garc'ia

activity

20172025

most citedOn perfect powers that are sums of cubes of a three term arithmetic progression

10 citations · 13 across the 4 of their papers we have counts for

collaborators

4 papers

math.NT2025

Computing rational solutions to $A x^{p} + B y^{p} + C z^{p} = 0$

Alejandro Argáez-García

In this survey, we studied the possibility of finding rational solutions to the equation $A x^{p} + B y^{p} + C z^{p} = 0$ via its attached hyperelliptic curve $Y^{2} = X^{p} + A^{2} (B C)^{p - 1} /4$ and its r…

math.NT2024

On the solutions to $A x^{p} + B y^{p} + C z^{p} = 0$ over quadratic fields

Alejandro Argáez-García, Luis Elí Pech-Moreno

We provide the necessary conditions for the existence of solutions $(x, y, z)$ to $A x^{p} + B y^{p} + C z^{p} = 0$ over any quadratic number field $K$ with $A, B, C$ pth powerfree integer numbers. W…

math.NT2017★ 10 cited

On perfect powers that are sums of cubes of a three term arithmetic progression

Alejandro Argáez-García, Vandita Patel

Using only elementary arguments, Cassels and Uchiyama (independently) determined all squares that are sums of three consecutive cubes. Zhongfeng Zhang extended this result and dete…

math.NT2017★ 3 cited

Black Box Galois Representations

Alejandro Argáez-García, John Cremona

We develop methods to study $2$ -dimensional $2$ -adic Galois representations $ρ$ of the absolute Galois group of a number field $K$ , unramified outside a known finite set of primes…

Computing rational solutions to Axp+Byp+Czp=0

On the solutions to Axp+Byp+Czp=0 over quadratic fields

On perfect powers that are sums of cubes of a three term arithmetic progression

Black Box Galois Representations

Computing rational solutions to $A x^{p} + B y^{p} + C z^{p} = 0$

On the solutions to $A x^{p} + B y^{p} + C z^{p} = 0$ over quadratic fields