The primitive solutions to the Diophantine equation
2X4 + Y4 =Z3

Gustav Söderlund
Notes on Number Theory and Discrete Mathematics
Print ISSN 1310–5132, Online ISSN 2367–8275
Volume 23, 2017, Number 2, Pages 36—44
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Gustav Söderlund
Kettilsgatan 4A 582 21 Linköping, Sweden

Abstract

We find all primitive non-zero integer solutions to the title equation, namely (x, y, z) =(±5,±3, 11). The proofs involved are based solely on elementary methods with no use of computers and the elliptic curve machinery.

Keywords

  • Diophantine equations
  • Primitive non-zero solutions

AMS Classification

  • 11D41

References

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Cite this paper

Söderlund, G. (2017). The primitive solutions to the Diophantine equation 2X4 + Y4 =Z3. Notes on Number Theory and Discrete Mathematics, 23(2), 36-44.

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