Solutions to some congruence equations via suborbital graphs

Güler, Bahadır Özgür; Kör, Tuncay; Şanlı, Zeynep

doi:10.1186/s40064-016-3016-5

Cited by 8 publications

(4 citation statements)

References 18 publications

(19 reference statements)

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“…Then, nontransitive cases have been examined to reach the general statement [7,10,11]. An interesting contribution of these studies was that the action of normalizer offers solutions for some congruence equations dealing with the sizes of circuits in the suborbital graph [8]. In this paper, we continue to examine some new cases.…”

Section: Motivationmentioning

confidence: 98%

On congruence equations arising from suborbital graphs

Güler¹,

Beşenk²,

Kader³

2019

Turk J Math

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In this paper we deal with congruence equations arising from suborbital graphs of the normalizer of Γ0(m) in P SL(2, R) . We also propose a conjecture concerning the suborbital graphs of the normalizer and the related congruence equations. In order to prove the existence of solution of an equation over prime finite field, this paper utilizes the Fuchsian group action on the upper half plane and Farey graphs properties.

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Section: Motivationmentioning

confidence: 98%

On congruence equations arising from suborbital graphs

Güler¹,

Beşenk²,

Kader³

2019

Turk J Math

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“…al. studied on the solutions of congruence equations that come from the action of the normalizer of Γ 0 (N ) via suborbital graphs [4,2]. With the similar notion, it is obtained some relationships Fibonacci numbers and suborbital graphs in the study [6,17].…”

Section: Introductionmentioning

confidence: 98%

Solutions to Pell's Equation via Suborbital Graphs

Köroğlu

2023

Preprint

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“…al. studied on solutions of congruence equations that come from the action of the normalizer of Γ 0 (n) via suborbital graphs [3].…”

Section: Introductionmentioning

confidence: 99%

Some group actions and Fibonacci numbers

Şanlı¹,

Köroğlu²

2022

Communications Faculty of Science University of Ankara Series A1Mathematics and Statistics

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The Fibonacci sequence has many interesting properties and studied by many mathematicians. The terms of this sequence appear in nature and is connected with combinatorics and other branches of mathematics. In this paper, we investigate the orbit of a special subgroup of the modular group. Taking0, we determined the orbit {T r c (∞) : r ∈ N}. Each rational number of this set is the form Pr(c)/Qr(c), where Pr(c) and Qr(c) are the polynomials in Z[c]. It is shown that Pr(1), and Qr(1) the sum of the coefficients of the polynomials Pr(c) and Qr(c) respectively, are the Fibonacci numbers, where Pr(c) = r s=0 2r − s s c 2r−2s + r s=1 2r − s s − 1 c 2r−2s+1 and Qr(c) = r s=1 2r − s s − 1 c 2r−2s+2 .

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Solutions to some congruence equations via suborbital graphs

Abstract: We relate the connection between the sizes of circuits in suborbital graph for the normalizer of in PSL(2,) and the congruence equations arising from related group action. We give a number theoretic result which says that all prime divisors of for any integer u must be congruent to .

Cited by 8 publications

References 18 publications

On congruence equations arising from suborbital graphs

On congruence equations arising from suborbital graphs

Solutions to Pell's Equation via Suborbital Graphs

Some group actions and Fibonacci numbers

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