Generalized Lucas Numbers of the form $wx^{2}$ and $wV_{m}x^{2}$

Duman, Merve Güney; Öğüt, Ümmügülsüm; Keski̇n, Refi̇k

doi:10.14492/hokmj/1537948825

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2023

2024

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Cited by 3 publications

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“…Other results related to the solutions of such equations connected to some sequences can be found in, e.g. [Ait-Amrane, 2017], [S¸iar] 2016, [Duman, 2018] and [Kiss, 1993].…”

Section: Introductionmentioning

confidence: 99%

The Generalized Lucas Primes in the Landau’s and Shanks’ Conjectures

Athab

Hashim

2023

jmss

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Landau’s conjecture and Shanks’ conjecture state that there are infinitely many prime numbers of the forms x2+1 and x4+1 for some nonzero integer , respectively. In this paper, we present a technique for studying whether or not there are infinitely many prime numbers of the form x2+1 or x4+1 derived from some Lucas sequences of the first kind {Un(P,Q)} (or simply, {Un}) or the second kind {Vn(P,Q)} (or simply, {Vn}) , where P greater or equal to 1 and Q= 1 or -1. Furthermore, as applications we represent the procedure of this technique in case of x is either an integer or a Lucas number of the first or the second kind with x greater or equal to 1 and 1 less or equal to P less or equal to 20.

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“…Other results related to the solutions of such equations connected to some sequences can be found in, e.g. [Ait-Amrane, 2017], [S¸iar] 2016, [Duman, 2018] and [Kiss, 1993].…”

Section: Introductionmentioning

confidence: 99%