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 \((n^2+1)/2\) whose sum is equal to \(\delta n+\varepsilon\), in the case when \(\delta\) and \(\varepsilon\) are even, or more precisely in the case in which \(\delta\equiv\varepsilon+2\equiv0\) or \(2 \pmod{4}\). We will completely solve the cases \(\delta=2, \delta=4\) and \(\varepsilon=0\).