The equation $(x-d)^5 + x^5 + (x+d)^5 = y^n$

preprint2020arXivOpen access

In this paper, we solve the equation of the title under the assumption that $\gcd(x,d)=1$ and $n\geq 2$ . This generalizes earlier work of the first author, Patel and Siksek [BPS16]. Our main tools include Frey-Hellegouarch curves and associated modular forms, and an assortment of Chabauty-type techniques for determining rational points on curves of small positive genus.

Explore this paper’s authors, topics and related work.

Building this map preview

BZPEER is loading the nearby papers, people, topics and institutions for this page.

Write a reviewWrite

No reviews yet.

Add a commentWrite

No comments yet.

The equation $(x-d)^5 + x^5 + (x+d)^5 = y^n$

Abstract

Connections

Building this map preview

Reviews 0

Discussion 0

The equation (x−d)5+x5+(x+d)5=yn(x-d)^5 + x^5 + (x+d)^5 = y^n(x−d)5+x5+(x+d)5=yn

Abstract

Connections

Building this map preview

Reviews 0

Discussion 0

The equation $(x-d)^5 + x^5 + (x+d)^5 = y^n$