engleski

Two divisors of (n^2+1)/2 summing up to δn + δ ± 2, δ even

We prove there exist infinitely many odd integers n for which there exists a pair of positive divisors d1, d2 of (n^2+1)/2 such that d1 + d2 = δn + ε for ε = δ + 2, where δ is an even positive integer. Furthermore, we deal with the same problem where ε = δ - 2 and δ ≡ 4, 6 (mod 8). Using different approaches and methods we obtain similar but conditional results since the proofs rely on Schinzel’s Hypothesis H.

Sum of divisors ; continued fractions ; Pell equation ; Legendre symbol

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