Uchiyama's conjecture on sums of squares

Tim Trudgian

Uchiyama's conjecture on sums of squares

Number Theory 2017-12-21 v1

Authors: Tim Trudgian

Abstract

Uchiyama showed that every interval $(n, n + c n^{1/4})$ contains an integer that is the sum of two squares, where $c= 2^{3/2}$ . He also conjectured a minimal value of $c$ such that the above statement still holds. We investigate this claim.

Keywords

uchiyama conjecture sums of two squares intervals number theory

Cite

@article{arxiv.1712.07243,
  title  = {Uchiyama's conjecture on sums of squares},
  author = {Tim Trudgian},
  journal= {arXiv preprint arXiv:1712.07243},
  year   = {2017}
}

Comments

To the Australian Test Cricket selectors, to whom I am indebted a slice of humble pie, after they ignored the strident remonstrances of TS Trudgian and included MR Marsh in the team

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