Profile URL: https://hdl.handle.net/20.500.13091/11938
Job Title:Prof. Dr.
Email Address:nirmak@ktun.edu.tr
Main Affiliation:02.05. Department of Engineering Basic Sciences
Status: Current Staff
ORCID:
0000-0003-0409-4342
0000-0003-0409-4342Scopus ID:
24477018800
24477018800YÖK Akademik: 1446C967B0D2B64D
Google Scholar:
Mos9rXMAAAAJ
Mos9rXMAAAAJWeb of Science ID:
ABF-7481-2021
ABF-7481-2021Name Variants:
Irmak, N.
20 results
Scholarly Output Search Results
Now showing 1 - 10 of 20
Article Citation - Scopus: 1Schreier Multisets and the S-Step Fibonacci Sequences(Colgate University, 2024) Chu, H.V.; Irmak, N.; Miller, S.J.; Szalay, L.; Zhang, S.X.Inspired by the surprising relationship (due to A. Bird) between Schreier sets and the Fibonacci sequence, we introduce Schreier multisets and connect these multisets with the s-step Fibonacci sequences, defined, for each s ≥ 2, as: F(s) 2−s=· · ·= F(s)0 = 0, F(s)1 = 1, and Fn(s) = F(s)n−1+· · ·+Fn−s,(s) for n ≥ 2. Next, we use Schreier-type conditions on multisets to retrieve a family of sequences which satisfy a recurrence of the form a(n) = a(n − 1) + a(n − u), with a(n) = 1 for n = 1, …, u. Finally, we study nonlinear Schreier conditions and show that these conditions are related to integer decompositions, each part of which is greater than the number of parts raised to some power. © 2024, Colgate University. All rights reserved.Article On K- Generalized Fibonacci Diophantine Triples(Univ Osijek, dept Mathematics, 2024) Irmak, NurettinFor n, k >= 2, the k-generalized Fibonacci sequence {F-n((k))}is defined by each term being the sum of the k preceding terms with the initial values 0,0,. . . , 0, 1 (k terms). In this paper, we prove that the system ab + 1 = F-x((k)) ac + 1 = F-y((k)) bc + 1 = F-z((k)) has no solution for 1 <= a < b < c with a <= 10(3) and some positive integers x, y and z.Article Citation - WoS: 1Citation - Scopus: 2On square Tribonacci Lucas numbers(Hacettepe University, 2021-12-14) Irmak, NurettinThe Tribonacci-Lucas sequence {Sn} is defined by the recurrence relation Sn+3 = Sn+2 + Sn+1 + Sn with S0 = 3, S1 = 1, S2 = 3. In this note, we show that 1 is the only perfect square in Tribonacci-Lucas sequence for (Formula presented) (mod 32) and (Formula presented) (mod 96). © 2021, Hacettepe University. All rights reserved.Article Factorials as Repdigits in Base B(Bulgarian Acad Science, 2022) Irmak, Nurettin; Togbe, AlainLet b is an element of {2, 3, ..., 9}. In this paper, we show that the solutions of the equation (x)(b) = m! are (11)(5) = 3!, (33)(7) = (44)(5) = 4!, where (x)(b) has at least two digits.Article A Novel Summation Identity by Using Delannoy Triangle(Ankara University Faculty of Science, 2026) Belbachir, Hacéne; Irmak, Nurettin; Amrouche, SaidIn this paper, we study the balancing and co-balancing problems for the coefficients located along the direction (1, -1) of the Delannoy triangle. Motivated by our search for the solutions of balancing problem, we give a novel identity on the Delannoy triangle.Article Citation - Scopus: 4The K-Generalized Lucas Numbers Close To a Power of 2(Walter De Gruyter Gmbh, 2023) Açıkel, Abdullah; Irmak, Nurettin; Szalay, LaszloLet k >= 2 be a fixed integer. The k-generalized Lucas sequence {L-n((k))}(n)>=(0) starts with the positive integer initial values k, 1, 3, ..., 2(k-1)-1, and each term afterward is the sum of the k consecutive preceding elements. An integer n is said to be close to a positive integer m if n satisfies |n-m| < root m. In this paper, we combine these two concepts. We solve completely the diophantine inequality |L-n((k)) - 2(m) | < 2(m/2) in the non-negative integers k, n, and m. This problem is equivalent to the resolution of the equation L-n((k)) = 2(m) + t with the condition |t| < 2(m/2), t is an element of Z. We also discovered a new formula for L-n((k)) which was very useful in the investigation of one particular case of the problem.Article On the Incompleted Sequences(2026) Kurt, Ebru Sena; Irmak, NurettinIn this study, Fibonacci, Lucas, and generalized forms of these sequences are examined. In the first chapter, definitions of Fibonacci and Lucas number sequences are provided, and some of their properties are analyzed. In the second chapter, incomplete Fibonacci and Lucas numbers are analyzed. Finally, in the third chapter, incomplete Fibonacci and Lucas numbers with arithmetic indices are defined and new relations are obtainedArticle The Diophantine Equation Ln(k)=(2a-1)(2b-1)(Springer, 2025) Irmak, Nurettin; Luca, FlorianLet k >= 2 be a fixed integer. The k-generalized Lucas sequence {Ln(k)}n >= 0 starts with the positive integer initial values k, 1, 3, ..., 2k-1-1, and each term afterward is the sum of the k consecutive preceding elements. In this paper, we find all solutions of the equation Ln(k)=(2a-1)(2b-1) in integers n >= 2,k >= 2, b >= a >= 0\.Article Generalized Tribonacci Diophantine Quadruples(Editura Acad Romane, 2021) Irmak, NurettinLet (t(n))(n >= 0) be defined by the recurrence t(n) = Atn-1 + t(n-2) + t(n-3) with t(0) = 0, t(1) = 1, t(2) = A and A >= 2 integer. In this paper, we prove that there does not exist integers 1 <= a(1) < a(2) < a(3) < a(4) such that a(1)a(2) + 1, a(2)a(3) + 1, a(3)a(4) + 1 and a(1)a(4) + 1 are Tribonacci numbers.Article On the Equation Fn-Fm=Fta(Springer Int Publ Ag, 2025-08-18) Irmak, Nurettin; Szalay, LaszloLet Fn denote nth Fibonacci number. In this paper, we show that the equation Fn-Fm=Fta has no solution in the integers n, m, t, a satisfying the conditions 6 <= t, 2 <= a <= t, and 3 <= n-m. This paper generalizes some previous results.
Research Topics
Domains
Physical Sciences
Fields
Physics and AstronomyMathematics
Subfields
Statistical and Nonlinear PhysicsAlgebra and Number TheoryMathematical PhysicsDiscrete Mathematics and CombinatoricsGeometry and Topology
Specific Research Areas
Advanced Mathematical Theories and Applications
Advanced Mathematical Identities
Advanced Mathematical Theories
Advanced Combinatorial Mathematics
Mathematics and Applications
Sustainable Development Goals
SDG data is not available
Documents
40
Citations
132
h-index
5
Documents
0
Citations
0
Publication Collaboration
| Affiliation Name | Count |
|---|---|
| Niğde Ömer Halisdemir Üniversitesi | 17 |
| Konya Technical University | 10 |
| University of Sopron | 6 |
| J. Selye University | 4 |
| Sambalpur University | 2 |
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Data obtained from OpenAlex
| Journal | Count |
|---|---|
| Turkish Journal of Mathematics | 3 |
| Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics | 1 |
| Communications Faculty of Sciences University of Ankara Series A1: Mathematics and Statistics | 1 |
| De Gruyter Proceedings in Mathematics -- Integers Conference on Combinatorial Number Theory 2023 -- 2023-05-17 through 2023-05-20 -- Athens -- 214204 | 1 |
| Hacettepe Journal of Mathematics and Statistics | 1 |
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Scholarly Output
20
Articles
19
Views / Downloads
20/61
Supervised MSc Theses
0
Supervised PhD Theses
0
WoS Citation Count
10
Scopus Citation Count
14
Patents
0
Projects
0
WoS Citations per Publication
0.50
Scopus Citations per Publication
0.70
Open Access Source
12
Supervised Theses
0
Scopus Quartile Distribution
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