A note on the Fermat quartic 34x4+y4=z4

Gustaf Söderlund
Notes on Number Theory and Discrete Mathematics
Print ISSN 1310–5132, Online ISSN 2367–8275
Volume 26, 2020, Number 4, Pages 103–105
DOI: 10.7546/nntdm.2020.26.4.103-105
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Gustaf Söderlund
Kettilsgatan 4A 58221 Linköping, Sweden

Abstract

We show that the only primitive non-zero integer solutions to the Fermat quartic 34x4+y4=z4 are (x,y,z) = (± 2, ± 3, ± 5). The proofs are based on a previously given complete solution to another Fermat quartic namely x4+y4=17z4.

Keywords

  • Fermat quartics
  • Diophantine equations
  • Primitive non-zero solutions

2010 Mathematics Subject Classification

  • 11D41

References

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  3. Flynn, E. V., & Wetherell, J. L. (2001). Covering collections and a challenge of Serre, Acta Arithmetica, 98, 197–205.
  4. Sally J. D., & Sally, P. J. (2007). Roots to Research: A Vertical Development of Mathematical Problems, American Mathematical Society.

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Cite this paper

Söderlund, G. (2020). A note on the Fermat quartic 34x4+y4=z4. Notes on Number Theory and Discrete Mathematics, 26 (4), 103-105, DOI: 10.7546/nntdm.2020.26.4.103-105.

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