A note on consecutive sums of two squares
Bulletin Polish Acad. Sci. Math.
MSC: Primary 11D09
DOI: 10.4064/ba250629-20-1
Published online: 22 January 2026
Abstract
The numbers $n$ for which both $n-2$ and $n+2$ are sums of two integral squares are characterized in two ways. These characterizations are applied to draw some corollaries on three consecutive sums of two squares. The divergence of the series $$ \sum_{a,b,c,d\in \mathbb Z,\, ad-bc=1}\frac{1}{a^2+b^2+c^2+d^2} $$ is also proved.
