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On the Diophantine Equation $p^x + p^y = z^{2n}$

Number Theory 2017-09-07 v1
Authors: Dibyajyoti Deb
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Abstract

In an earlier paper, Tatong and Suvarnamani explores the Diophantine equation px+py=z2p^x + p^y = z^2 for a prime number pp. In that paper they find some solutions to the equation for p=2,3p=2, 3. In this paper, we look at a general version of this equation and solve it completely.

Keywords

Diophantine equation prime number integer solutions exponential equation number theory complete solution

Cite

@article{arxiv.1709.01814,
  title  = {On the Diophantine Equation $p^x + p^y = z^{2n}$},
  author = {Dibyajyoti Deb},
  journal= {arXiv preprint arXiv:1709.01814},
  year   = {2017}
}

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