Izvorni znanstveni članak

https://doi.org/10.21857/yk3jwhrjd9

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

Sanda Bujačić Babić orcid.org/0000-0001-8842-3830 ; Department of Mathematics, University of Rijeka, Radmile Matejčić 2, 51000 Rijeka, Croatia

Sažetak

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.

Ključne riječi

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

Hrčak ID:

206194

URI

https://hrcak.srce.hr/206194

Datum izdavanja:

28.9.2018.

Posjeta: 1.302 *