Archiv der Mathematik

, Volume 102, Issue 5, pp 411–421 | Cite as

The generalised Fermat equation x 2 + y 3 = z 15

Article

Abstract

We determine the set of primitive integral solutions to the generalised Fermat equation x 2 + y 3 = z 15. As expected, the only solutions are the trivial ones with xyz = 0 and the non-trivial one (x, y, z) = (± 3, −2, 1).

Mathematics Subject Classification (2000)

Primary 11G30 Secondary 11G35 14K20 14C20 

Keywords

Hyperelliptic curves Descent Fermat–Catalan Generalised Fermat equation 

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Copyright information

© Springer Basel 2014

Authors and Affiliations

  1. 1.Mathematics InstituteUniversity of WarwickCoventryUnited Kingdom
  2. 2.Mathematisches InstitutUniversität BayreuthBayreuthGermany

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