On integers which are representable as sums of large squares

Abstract

We prove that the greatest positive integer that is not expressible as a linear combination with integer coefficients of elements of the set $\{n^2,(n+1{)}^2,\dots \}$ 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.

arXiv comment6 pages. To appear in International Journal of Number Theory