Alejandro Argáez-García

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

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math.NT2023

Nontrivial solutions to the Fermat equation $x^{3} + y^{3} = k z^{3}$ over quadratic number fields

Alejandro Argaez-Garcia, Javier Diaz-Vargas, Luis Eli Pech-Moreno

We give sufficient conditions to determine the existence of nontrivial solutions to the Fermat equation $x^{3} + y^{3} = k z^{3}$ over $Q (d)$ by constructing a relationship wi…

math.NT2019

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

Alejandro Argáez-García, Vandita Patel

We prove that the equation $(x - 3 r)^{3} + (x - 2 r)^{3} + (x - r)^{3} + x^{3} + (x + r)^{3} + (x + 2 r)^{3} + (x + 3 r)^{3} = y^{p}$ only has solutions which satisfy $x y = 0$ for $1 \leq r \leq 1 0^{6}$ and $p \geq 5$ prime…

math.NT2019★ 5 cited

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

Alejandro Argáez-García

We prove that the equation $(x - 2 r)^{3} + (x - r)^{3} + x^{3} + (x + r)^{3} + (x + 2 r)^{3} = y^{p}$ only has solutions which satisfy $x y = 0$ for $1 \leq r \leq 1 0^{6}$ and $p \geq 5$ prime.

Nontrivial solutions to the Fermat equation x3+y3=kz3 over quadratic number fields

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

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

Nontrivial solutions to the Fermat equation $x^{3} + y^{3} = k z^{3}$ over quadratic number fields