A+ CATEGORY SCIENTIFIC UNIT

PDF files of articles are only available for institutions which have paid for the online version upon signing an Institutional User License.

A new diophantine equation involving fifth powers

Volume 202 / 2022

Ajai Choudhry, Oliver Couto Acta Arithmetica 202 (2022), 43-53 MSC: Primary 11D41. DOI: 10.4064/aa210419-4-7 Published online: 26 November 2021

Abstract

We obtain two parametric solutions of the hitherto unsolved diophantine equation $(x_1^5+x_2^5)(x_3^5+x_4^5)=(y_1^5+y_2^5)(y_3^5+y_4^5)$. Further, we show, using elliptic curves, that there exist infinitely many parametric solutions of the aforementioned diophantine equation, and they can be effectively computed.

Authors

  • Ajai Choudhry13/4 A Clay Square
    Lucknow 226001, India
    e-mail
  • Oliver CoutoApartment 501, 2166 Lakeshore Road Burlington, Ontario, L7R 2B6, Canada
    e-mail

Search for IMPAN publications

Query phrase too short. Type at least 4 characters.

Rewrite code from the image

Reload image

Reload image