Two divisors of (n^2+1)/2 summing up to {\delta}n+{\epsilon}, for {\delta} and {\epsilon} even

In this paper we are dealing with the problem of the existence of two divisors of $(n^2+1)\mathrm{/}2$ whose sum is equal to $\delta n+\epsilon$, in the case when $\delta$ and $\epsilon$ are even, or more precisely in the case in which $\delta \equiv \epsilon +2\equiv 0$ or $2(\mathrm{m}\mathrm{o}\mathrm{d}4)$. We will completely solve the cases $\delta =2,\delta =4$ and $\epsilon =0$.