On a class of generalized Fermat equations of signature (2,2n,3)


Chałupka K., Dąbrowski A., SOYDAN G.

Journal of Number Theory, vol.234, pp.153-178, 2022 (Journal Indexed in SCI) identifier identifier

  • Publication Type: Article / Article
  • Volume: 234
  • Publication Date: 2022
  • Doi Number: 10.1016/j.jnt.2021.06.019
  • Title of Journal : Journal of Number Theory
  • Page Numbers: pp.153-178
  • Keywords: Diophantine equation, Modular form, Elliptic curve, Galois representation, Chabauty method, DIOPHANTINE EQUATIONS

Abstract

© 2021 Elsevier Inc.We consider the Diophantine equation 7x2+y2n=4z3. We determine all solutions to this equation for n=2,3,4 and 5. We formulate a Kraus type criterion for showing that the Diophantine equation 7x2+y2p=4z3 has no non-trivial proper integer solutions for specific primes p>7. We computationally verify the criterion for all primes 7