Ahmet Emin
Current Organizations / Institutes
The organizations/institutes from the scholar's latest article
Research Subjects
Ahmet Emin has a total of 5 co-authors. Here are the top co-authors by number of shared publications:
- Ahmet Daşdemir
Department of Mathematics, Faculty of Science, Kastamonu University, Kastamonu, Türkiye
5 shared publications - Ümit Sarp
Continuing Education Application and Research Center (IKCUSEM), Izmir Katip Celebi University, 35620 Izmir, Türkiye
2 shared publications - Bilal Demir
Department of Mathematics, Necatibey Faculty of Education, Balıkesir University , 10100 Balıkesir , Türkiye
1 shared publication - Firat Ates
Balıkesir University
1 shared publication - Seyran Ibrahimov
Eastern Mediterranean University
1 shared publication
Latest Publications
- Open Access
- 26 February 2026
- Published by Prof. Marin Drinov Publishing House of BAS (Bulgarian Academy of Sciences) in Notes on Number Theory and Discrete Mathematics
- Vol. 32 (1)
Diophantine equations for additive Pell numbers in Pell, Pell–Lucas, and Modified Pell numbers
This paper investigates the Diophantine equations arising from ternary additive problems of Pell, Pell–Lucas, and Modified Pell numbers. Specifically, we characterize all integer solutions to the equation ${P_n} + {P_m} + {P_r} = {X_k}$, $X \in \left\{ {{P},{Q},{R}} \right\}$, where ${P_i}$, ${Q_i}$, and ${R_i}$ denote the $i$-th terms of the Pell, Pell–Lucas, and Modified Pell sequences, respectively. By leveraging recurrence relations, Binet's formulas, and Carmichael's Primitive Divisor Theorem, we provide the first complete classification of solutions to this ternary additive problem. Our results reveal several parametric and singular solutions. Furthermore, we reduce prior results to binary sums of the form ${P_n} + {P_m} = {X_k}$ as special instances of our framework.- 26 February 2026
- Published by Prof. Marin Drinov Publishing House of BAS (Bulgarian Academy of Sciences) in Notes on Number Theory and Discrete Mathematics
- Vol. 32 (1)
Open AccessDiophantine equations for additive Pell numbers in Pell, Pell–Lucas, and Modified Pell numbers
This paper investigates the Diophantine equations arising from ternary additive problems of Pell, Pell–Lucas, and Modified Pell numbers. Specifically, we characterize all integer solutions to the equation ${P_n} + {P_m} + {P_r} = {X_k}$, $X \in \left\{ {{P},{Q},{R}} \right\}$, where ${P_i}$, ${Q_i}$, and ${R_i}$ denote the $i$-th terms of the Pell, Pell–Lucas, and Modified Pell sequences, respectively. By leveraging recurrence relations, Binet's formulas, and Carmichael's Primitive Divisor Theorem, we provide the first complete classification of solutions to this ternary additive problem. Our results reveal several parametric and singular solutions. Furthermore, we reduce prior results to binary sums of the form ${P_n} + {P_m} = {X_k}$ as special instances of our framework. - 31 December 2025
- Published by Adiyaman University in Adıyaman University Journal of Science
- Vol. 15 (2) , 217-227
On the Solutions of the Diophantine Equations P_k=R_m R_n and R_k=P_m P_n
This study aims to find all possible solutions (k,m,n) of the Diophantine equations P_k=R_m R_n and R_k=P_m P_n . Our proof is conducted with the famous Matveev theorem and Dujella-Pethő reduction lemma.
- 31 December 2025
- Published by Adiyaman University in Adıyaman University Journal of Science
- Vol. 15 (2) , 217-227
On the Solutions of the Diophantine Equations P_k=R_m R_n and R_k=P_m P_n
This study aims to find all possible solutions (k,m,n) of the Diophantine equations P_k=R_m R_n and R_k=P_m P_n . Our proof is conducted with the famous Matveev theorem and Dujella-Pethő reduction lemma.
- 9 September 2025
- Published by Izmir UOD
- p. 331-339
On the Second Zagreb Index of Triangular Cycle Graphs
This study investigates the second Zagreb index 2 M G( ) of triangular cycle graphs, derived from the geometric arrangement of triangular numbers. The second Zagreb index, defined as the sum of the products of vertex degrees for adjacent vertices, provides insights into edge-based connectivity and branching patterns. By analyzing the structure of triangular cycle graphs, we classify edges based on vertex degrees ( 2 2 , 2 3 , or 3 3 ) and derive explicit formulas for the second Zagreb index. Our results, including the formula 2 2 M T n n n ( ( )) 2 20 37 for n 3 , enhance the understanding of these graphs' topological properties and their applications in network analysis and chemical graph theory.
- 9 September 2025
- Published by Izmir UOD
- p. 331-339
On the Second Zagreb Index of Triangular Cycle Graphs
This study investigates the second Zagreb index 2 M G( ) of triangular cycle graphs, derived from the geometric arrangement of triangular numbers. The second Zagreb index, defined as the sum of the products of vertex degrees for adjacent vertices, provides insights into edge-based connectivity and branching patterns. By analyzing the structure of triangular cycle graphs, we classify edges based on vertex degrees ( 2 2 , 2 3 , or 3 3 ) and derive explicit formulas for the second Zagreb index. Our results, including the formula 2 2 M T n n n ( ( )) 2 20 37 for n 3 , enhance the understanding of these graphs' topological properties and their applications in network analysis and chemical graph theory.
- Open Access
- 15 July 2025
- Published by Balikesir Universitesi Fen Bilimleri Enstitusu Dergisi in Balıkesir Üniversitesi Fen Bilimleri Enstitüsü Dergisi
- Vol. 27 (2) , 464-474
Diophantine equations on cross-multiplicative forms of the Pell and Pell-Lucas numbers
This study aims to explore all Pell numbers that are the product of two random Pell-Lucas numbers and all Pell-Lucas numbers that are the product of two random Pell numbers based on linear forms in logarithms of algebraic numbers using Matveev's theorem and Dujella - Pethő reduction lemma. Further, we find all the common terms of Pell and Pell-Lucas numbers and show that no Pell and no Pell-Lucas numbers can be written as a square of another.
- 15 July 2025
- Published by Balikesir Universitesi Fen Bilimleri Enstitusu Dergisi in Balıkesir Üniversitesi Fen Bilimleri Enstitüsü Dergisi
- Vol. 27 (2) , 464-474
Open AccessDiophantine equations on cross-multiplicative forms of the Pell and Pell-Lucas numbers
This study aims to explore all Pell numbers that are the product of two random Pell-Lucas numbers and all Pell-Lucas numbers that are the product of two random Pell numbers based on linear forms in logarithms of algebraic numbers using Matveev's theorem and Dujella - Pethő reduction lemma. Further, we find all the common terms of Pell and Pell-Lucas numbers and show that no Pell and no Pell-Lucas numbers can be written as a square of another.
- Open Access
- 1 January 2025
- Published by American Institute of Mathematical Sciences (AIMS) in AIMS Mathematics
- Vol. 10 (8) , 18524-18540
On the dynamics of the Fermat-like Diophantine equation involving Pell numbers
In this study, we investigated a Fermat-like Diophantine equation involving Pell numbers, specifically examining powers of two that can be represented as the sum of the $ x $-th powers of any two Pell numbers. To solve the equation $ {P^{x}_m} + {P^{x}_n} = {2^a} $ for $ x \geq 3 $, where $ m $, $ n $, $ x $, and $ a $ are non-negative integers, we employed Baker's theory of linear forms in logarithms, a modified version of the Baker-Davenport reduction method, and properties of continued fractions. Our results extend previous findings for $ x = 1 $ and $ x = 2 $, shedding light on the interplay between Pell numbers and powers of two in this exponential context.- 1 January 2025
- Published by American Institute of Mathematical Sciences (AIMS) in AIMS Mathematics
- Vol. 10 (8) , 18524-18540
Open AccessOn the dynamics of the Fermat-like Diophantine equation involving Pell numbers
In this study, we investigated a Fermat-like Diophantine equation involving Pell numbers, specifically examining powers of two that can be represented as the sum of the $ x $-th powers of any two Pell numbers. To solve the equation $ {P^{x}_m} + {P^{x}_n} = {2^a} $ for $ x \geq 3 $, where $ m $, $ n $, $ x $, and $ a $ are non-negative integers, we employed Baker's theory of linear forms in logarithms, a modified version of the Baker-Davenport reduction method, and properties of continued fractions. Our results extend previous findings for $ x = 1 $ and $ x = 2 $, shedding light on the interplay between Pell numbers and powers of two in this exponential context. - 30 November 2024
- Published by World Scientific Pub Co Pte Ltd in Asian-European Journal of Mathematics
- Vol. 18 (04)
On the exponential Diophantine equation Pm2 + Pn2 = 2a
This study investigates numbers that are powers of two and can be expressed as the sum of the squares of any two Pell numbers. We apply Baker’s theory of linear forms in logarithms of algebraic numbers, along with a variation of the Baker–Davenport reduction method, to solve the Diophantine equation [ ], where [ ], and [ ] are non-negative integers, as presented here. Furthermore, the maple[ ] codes used in the computations made throughout the paper are also shared.
- 30 November 2024
- Published by World Scientific Pub Co Pte Ltd in Asian-European Journal of Mathematics
- Vol. 18 (04)
On the exponential Diophantine equation Pm2 + Pn2 = 2a
This study investigates numbers that are powers of two and can be expressed as the sum of the squares of any two Pell numbers. We apply Baker’s theory of linear forms in logarithms of algebraic numbers, along with a variation of the Baker–Davenport reduction method, to solve the Diophantine equation [ ], where [ ], and [ ] are non-negative integers, as presented here. Furthermore, the maple[ ] codes used in the computations made throughout the paper are also shared.
- Open Access
- 29 November 2024
- Published by Bilecik Seyh Edebali Universitesi Fen Bilimleri Dergisi in Bilecik Şeyh Edebali Üniversitesi Fen Bilimleri Dergisi
- Vol. 11 (2) , 325-334
Groupoid and Semigroup Construction on Isosceles Triangular Numbers
Basic information about figurative numbers is provided. Then, information about isosceles triangular numbers, one of the two-dimensional figurative numbers, is given. It also includes information about algebraic structures and their definitions. Additionally, a binary operation that includes k -isosceles triangular numbers is presented, and the study investigates whether the algebraic structures defined with this operation form a groupoid or semigroup. Also, two examples are given that satisfy the results at the end of the paper.
- 29 November 2024
- Published by Bilecik Seyh Edebali Universitesi Fen Bilimleri Dergisi in Bilecik Şeyh Edebali Üniversitesi Fen Bilimleri Dergisi
- Vol. 11 (2) , 325-334
Open AccessGroupoid and Semigroup Construction on Isosceles Triangular Numbers
Basic information about figurative numbers is provided. Then, information about isosceles triangular numbers, one of the two-dimensional figurative numbers, is given. It also includes information about algebraic structures and their definitions. Additionally, a binary operation that includes k -isosceles triangular numbers is presented, and the study investigates whether the algebraic structures defined with this operation form a groupoid or semigroup. Also, two examples are given that satisfy the results at the end of the paper.
- 30 September 2024
- Published by Anadolu Universitesi Bilim ve Teknoloji Dergisi-A: Uygulamali Bilimler ve Muhendislik in Eskişehir Technical University Journal of Science and Technology A - Applied Sciences and Engineering
- Vol. 25 (3) , 407-414
FIBONACCI AND LUCAS NUMBERS AS PRODUCTS OF THEIR ARBITRARY TERMS
This study presents all solutions to the Diophantine equations F_k=L_m L_n and L_k=F_m F_n. To be clear, the Fibonacci numbers that are the product of two arbitrary Lucas numbers and the Lucas numbers that are the product of two arbitrary Fibonacci numbers are determined herein. The results under consideration are proven by using the Dujella-Pethő lemma in coordination with Matveev's theorem. All common terms of the Fibonacci and Lucas numbers are determined. Further, the Lucas-square Fibonacci and Fibonacci-square Lucas numbers are given.
- 30 September 2024
- Published by Anadolu Universitesi Bilim ve Teknoloji Dergisi-A: Uygulamali Bilimler ve Muhendislik in Eskişehir Technical University Journal of Science and Technology A - Applied Sciences and Engineering
- Vol. 25 (3) , 407-414
FIBONACCI AND LUCAS NUMBERS AS PRODUCTS OF THEIR ARBITRARY TERMS
This study presents all solutions to the Diophantine equations F_k=L_m L_n and L_k=F_m F_n. To be clear, the Fibonacci numbers that are the product of two arbitrary Lucas numbers and the Lucas numbers that are the product of two arbitrary Fibonacci numbers are determined herein. The results under consideration are proven by using the Dujella-Pethő lemma in coordination with Matveev's theorem. All common terms of the Fibonacci and Lucas numbers are determined. Further, the Lucas-square Fibonacci and Fibonacci-square Lucas numbers are given.
- Open Access
- 29 August 2024
- Published by Prof. Marin Drinov Publishing House of BAS (Bulgarian Academy of Sciences) in Proceedings of the Bulgarian Academy of Sciences
- Vol. 77 (8) , 1128-1137
On the Diophantine Equation ${L^2_m}+{L^2_n}=2^a$This study researches numbers that are powers of two and can be represented as the sum of the squares of any two Lucas numbers. We apply Baker's theory of linear forms in logarithms of algebraic numbers, combined with a variation of the Baker--Davenport reduction method, to solve the Diophantine equation $$L^2_m+L^2_n=2^a$$, where $$m$$, $$n$$ and $$a$$ are positive integers, as presented in this study.- 29 August 2024
- Published by Prof. Marin Drinov Publishing House of BAS (Bulgarian Academy of Sciences) in Proceedings of the Bulgarian Academy of Sciences
- Vol. 77 (8) , 1128-1137
Open AccessOn the Diophantine Equation ${L^2_m}+{L^2_n}=2^a$This study researches numbers that are powers of two and can be represented as the sum of the squares of any two Lucas numbers. We apply Baker's theory of linear forms in logarithms of algebraic numbers, combined with a variation of the Baker--Davenport reduction method, to solve the Diophantine equation $$L^2_m+L^2_n=2^a$$, where $$m$$, $$n$$ and $$a$$ are positive integers, as presented in this study.