Original scientific paper
https://doi.org/10.21857/yk3jwhrjd9
Two divisors of (n^2+1)/2 summing up to δn + δ ± 2, δ even
Sanda Bujačić Babić
; Department of Mathematics, University of Rijeka, Radmile Matejčić 2, 51000 Rijeka, Croatia
Abstract
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.
Keywords
Sum of divisors; continued fractions; Pell equation; Legendre symbol
Hrčak ID:
206194
URI
Publication date:
28.9.2018.
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