Another generalization of a theorem of Baker and Davenport

Bo He; Ákos Pintér; Alain Togbe; Shichun Yang

Another generalization of a theorem of Baker and Davenport

Number Theory 2015-11-03 v2

Authors: Bo He , Ákos Pintér , Alain Togbe , Shichun Yang

Abstract

Dujella and Peth\H{o}, generalizing a result of Baker and Davenport, proved that the set $\{1, 3\}$ cannot be extended to a Diophantine quintuple. As a consequence of our main result, it is shown that the Diophantine pair $\{1, b\}$ cannot be extended to a Diophantine quintuple if $b-1$ is a prime.

Keywords

diophantine quintuple diophantine pair Baker-Davenport theorem generalization prime number diophantine set

Cite

@article{arxiv.1510.05579,
  title  = {Another generalization of a theorem of Baker and Davenport},
  author = {Bo He and Ákos Pintér and Alain Togbe and Shichun Yang},
  journal= {arXiv preprint arXiv:1510.05579},
  year   = {2015}
}

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