On integers which are representable as sums of large squares

Alessio Moscariello

On integers which are representable as sums of large squares

Number Theory 2015-04-14 v3

Authors: Alessio Moscariello

Abstract

We prove that the greatest positive integer that is not expressible as a linear combination with integer coefficients of elements of the set $\{n^2,(n+1)^2,\ldots \}$ is asymptotically $O(n^2)$ , verifying thus a conjecture of Dutch and Rickett. Furthermore we ask a question on the representation of integers as sum of four large squares.

Keywords

number theory sums of squares linear combinations asymptotic bounds frobenius problem integer representation

Cite

@article{arxiv.1408.1435,
  title  = {On integers which are representable as sums of large squares},
  author = {Alessio Moscariello},
  journal= {arXiv preprint arXiv:1408.1435},
  year   = {2015}
}

Comments

6 pages. To appear in International Journal of Number Theory

On integers which are representable as sums of large squares

Abstract

Keywords

Cite

Comments

Related papers