Generalized Lucas numbers of the form 11x2∓111x2∓111x^{2}\mp 1

Refik KESKİN; Ümmügülsüm ÖĞÜT

Article Details

Generalized Lucas numbers of the form 11x2∓111x2∓111x^{2}\mp 1

Authors:

Refik KESKİN | Ümmügülsüm ÖĞÜT

Publisher:

Hacettepe University

Main Topics:

Mathematics

Journal:

Hacettepe Journal of Mathematics and Statistics 2019 Vol.48 Issue 4, pp.1035-1045

Document Type:

Article

Publication Date:

8/2019

Document Language:

English

Document ID (Org No.):

2000451466

Frequency:

Bimonthly

eISSN:

2651-477X

pISSN:

2651-477X

Abstract:

 

Let P≥3P≥3P\geq3 be an integer and (Vn)(Vn)(V_{n}) denote generalized Lucas sequence defined by V0=2,V1=P,V0=2,V1=P,V_{0}=2,V_{1}=P, and Vn+1=PVn−Vn−1Vn+1=PVn−Vn−1V_{n+1}=PV_{n}-V_{n-1} for n≥1.n≥1.n\geq1. In this study, we solve the equation Vn=11x2∓1.Vn=11x2∓1.V_{n}=11x^{2}\mp1. We show that the equation Vn=11x2+1Vn=11x2+1V_{n}=11x^{2}+1 has a solution only when n=1n=1n=1 and P≡1(mod11)P≡1(mod11)P\equiv 1({mod}11). Moreover, we show that if the equation Vn=11x2−1Vn=11x2−1V_{n}=11x^{2}-1 has a solution, then P≡2(mod8)P≡2(mod8)P\equiv2({mod}8) and P≡−1(mod11).P≡−1(mod11).P\equiv-1({mod}11).

Article Details

Generalized Lucas numbers of the form 11x2∓111x2∓111x^{2}\mp 1

Authors: Refik KESKİN | Ümmügülsüm ÖĞÜT

Publisher: Hacettepe University

Main Topics: Mathematics

Journal: Hacettepe Journal of Mathematics and Statistics 2019 Vol.48 Issue 4, pp.1035-1045

Document Type: Article

Publication Date: 8/2019

Document Language: English

Document ID (Org No.): 2000451466

Frequency: Bimonthly

eISSN: 2651-477X

pISSN: 2651-477X

Issues

Authors:

Refik KESKİN | Ümmügülsüm ÖĞÜT

Publisher:

Hacettepe University

Main Topics:

Mathematics

Journal:

Hacettepe Journal of Mathematics and Statistics 2019 Vol.48 Issue 4, pp.1035-1045

Document Type:

Article

Publication Date:

8/2019

Document Language:

English

Document ID (Org No.):

2000451466

Frequency:

Bimonthly

eISSN:

2651-477X

pISSN:

2651-477X