Nejib Ghanmi

Scopus Publications

Numbers with empty rational Korselt sets
Nejib GHANMİ
Hacettepe Journal of Mathematics and Statistics, 2022
Let $N$ be a positive integer, and $\alpha=\dfrac{\alpha_{1}}{\alpha_{2}}\in \mathbb{Q}\setminus \{0,N\}$ with $\gcd(\alpha_{1}, \alpha_{2})=1$. $N$ is called an $\alpha$-Korselt number, equivalently $\alpha$ is said an $N$-Korselt base, if $\alpha_{2}p-\alpha_{1}$ divides $\alpha_{2}N-\alpha_{1}$ for every prime divisor $p$ of $N$. The set of $N$-Korselt bases in $\mathbb{Q}$ is denoted by $\mathbb{Q}$-$\mathcal{KS}(N)$ and called the set of rational Korselt bases of $N$.In this paper rational Korselt bases are deeply studied, where we give in details their belonging sets and their forms in some cases. This allows us to deduce that for each integer $n\geq 3$, there exist infinitely many squarefree composite numbers $N$ with $n$ prime factors and empty rational Korselt sets.
Novel Analysis of Fractional-Order Fifth-Order Korteweg-de Vries Equations
Ahmed B. Khoshaim, Muhammad Naeem, Ali Akgul, Nejib Ghanmi, Shamsullah Zaland
Journal of Mathematics, 2022
In this paper, the ρ -homotopy perturbation transformation method was applied to analysis of fifth-order nonlinear fractional Korteweg–de Vries (KdV) equations. This technique is the mixture form of the ρ -Laplace transformation with the homotopy perturbation method. The purpose of this study is to demonstrate the validity and efficiency of this method. Furthermore, it is demonstrated that the fractional and integer-order solutions close in on the exact result. The suggested technique was effectively utilized and was accurate and simple to use for a number of related engineering and science models.
A novel decision making technique based on spherical hesitant fuzzy yager aggregation information: Application to treat parkinson’s disease
Muhammad Naeem, , Aziz Khan, Shahzaib Ashraf, Saleem Abdullah, Muhammad Ayaz, Nejib Ghanmi, , , and
Aims Mathematics, 2022
<abstract><p>The concept of spherical hesitant fuzzy set is a mathematical tool that have the ability to easily handle imprecise and uncertain information. The method of aggregation plays a great role in decision-making problems, particularly when there are more conflicting criteria. The purpose of this article is to present novel operational laws based on the Yager t-norm and t-conorm under spherical hesitant fuzzy information. Furthermore, based on the Yager operational laws, we develop the list of Yager weighted averaging and Yager weighted geometric aggregation operators. The basic fundamental properties of the proposed operators are given in detail. We design an algorithm to address the uncertainty and ambiguity information in multi-criteria group decision making (MCGDM) problems. Finally, a numerical example related to Parkinson disease is presented for the proposed model. To show the supremacy of the proposed algorithms, a comparative analysis of the proposed techniques with some existing approaches and with validity test is presented.</p></abstract>
Connections on the rational Korselt set of pq
Nejib GHANMİ
Hacettepe Journal of Mathematics and Statistics, 2021
For a positive integer $N$ and $\\mathbb{A}$ a subset of $\\mathbb{Q}$, let $\\mathbb{A}$-$\\mathcal{KS}(N)$ denote the set of $\\alpha=\\dfrac{\\alpha_{1}}{\\alpha_{2}}\\in \\mathbb{A}\\setminus \\{0,N\\}$ verifying $\\alpha_{2}r-\\alpha_{1}$ divides $\\alpha_{2}N-\\alpha_{1}$ for every prime divisor $r$ of $N$. The set $\\mathbb{A}$-$\\mathcal{KS}(N)$ is called the set of $N$-Korselt bases in $\\mathbb{A}$. Let $p, q$ be two distinct prime numbers. In this paper, we prove that each $pq$-Korselt base in $\\mathbb{Z}\\setminus\\{ q+p-1\\}$ generates other(s) in $\\mathbb{Q}$-$\\mathcal{KS}(pq)$. More precisely, we will prove that if $(\\mathbb{Q}\\setminus\\mathbb{Z})$-$\\mathcal{KS}(pq)=\\emptyset$ then $\\mathbb{Z}$-$\\mathcal{KS}(pq)=\\{ q+p-1\\}$.
The Q -Korselt set of pq
Nejib Ghanmi
Periodica Mathematica Hungarica, 2020
Let $N$ be a positive integer, $\\mathbb{A}$ be a nonempty subset of $\\mathbb{Q}$ and $\\alpha=\\dfrac{\\alpha_{1}}{\\alpha_{2}}\\in \\mathbb{A}\\setminus \\{0,N\\}$. $\\alpha$ is called an $N$-Korselt base (equivalently $N$ is said an $\\alpha$-Korselt number) if $\\alpha_{2}p-\\alpha_{1}$ is a divisor of $\\alpha_{2}N-\\alpha_{1}$ for every prime $p$ dividing $N$. The set of all Korselt bases of $N$ in $\\mathbb{A}$ is called the $\\mathbb{A}$-Korselt set of $N$ and is simply denoted by $\\mathbb{A}$-$\\mathcal{KS}(N)$. Let $p$ and $q$ be two distinct prime numbers. In this paper, we study the $\\mathbb{Q}$-Korselt bases of $pq$, where we give in detail how to provide $\\mathbb{Q}$-$\\mathcal{KS}(pq)$. Consequently, we finish the incomplete characterization of the Korselt set of $pq$ over $\\mathbb{Z}$ given in [4], by supplying the set $\\mathbb{Z}$-$\\mathcal{KS}(pq)$ when $q <2p$.
On the Diophantine equation Cx2+ D= 2 yq
Nejib Ghanmi, Fadwa S. Abu Muriefah
Ramanujan Journal, 2020
Let C and D denote positive integers such that $$CD>1$$ . In this paper we investigate the solvability of the Diophantine equation $$Cx^{2}+D=2y^{q}$$ , in positive integers x, y and odd prime number q where $$CD\\not \\equiv 3 \\pmod 4$$ and CD is squarefree.
Korselt rational bases of prime powers
Nejib Ghanmi
Studia Scientiarum Mathematicarum Hungarica, 2019
Let N be a positive integer, be a subset of ℚ and . N is called an α-Korselt number (equivalently α is said an N-Korselt base) if α2p − α1 divides α2N − α1 for every prime divisor p of N. By the Korselt set of N over , we mean the set of all such that N is an α-Korselt number. In this paper we determine explicitly for a given prime number q and an integer l ∈ ℕ \\{0, 1}, the set and we establish some connections between the ql -Korselt bases in ℚ and others in ℤ. The case of is studied where we prove that is empty if and only if l = 2. Moreover, we show that each nonzero rational α is an N-Korselt base for infinitely many numbers N = ql where q is a prime number and l ∈ ℕ.
ℚ-Korselt numbers
Nejib GHANMI
Turkish Journal of Mathematics, 2018
Let α = α1 α2 ∈ Q \\ {0} ; a positive integer N is said to be an α -Korselt number (Kα -number, for short) if N ̸= α and α2p−α1 divides α2N −α1 for every prime divisor p of N . In this paper we prove that for each squarefree composite number N there exist finitely many rational numbers α such that N is a Kα -number and if α ≤ 1 then N has at least three prime factors. Moreover, we prove that for each α ∈ Q \\ {0} there exist only finitely many squarefree composite numbers N with two prime factors such that N is a Kα -number.
On williams numbers with three prime factors
Ibrahim Al-Rasasi, Nejib Ghanmi
Missouri Journal of Mathematical Sciences, 2013
Let $a\in \mathbb{Z}\setminus \{0\}$. A positive squarefree integer $N$ is said to be an $a$-Korselt number ($K_{a}$-number, for short) if $N\neq a$ and $p-a$ divides $N-a$ for each prime divisor $p$ of $N$. By an $a$-Williams number ($W_{a}$-number, for short) we mean a positive integer which is both an $a$-Korselt number and $(-a)$-Korselt number. This paper proves that for each $a$ there are only finitely many $W_{a}$-numbers with exactly three prime factors, as conjectured in 2010 by Bouallegue-Echi-Pinch.
The korselt set of pq
OTHMAN ECHI, NEJIB GHANMI
International Journal of Number Theory, 2012
Let α ∈ ℤ\\{0}. A positive integer N is said to be an α-Korselt number (Kα-number, for short) if N ≠ α and N - α is a multiple of p - α for each prime divisor p of N. By the Korselt set of N, we mean the set of all α ∈ ℤ\\{0} such that N is a Kα-number; this set will be denoted by [Formula: see text]. Given a squarefree composite number, it is not easy to provide its Korselt set and Korselt weight both theoretically and computationally. The simplest kind of squarefree composite number is the product of two distinct prime numbers. Even for this kind of numbers, the Korselt set is far from being characterized. Let p, q be two distinct prime numbers. This paper sheds some light on [Formula: see text].

RECENT SCHOLAR PUBLICATIONS

Research Article Novel Analysis of Fractional-Order Fifth-Order Korteweg–de Vries Equations
AB Khoshaim, M Naeem, A Akgul, N Ghanmi, S Zaland
2022
Numbers with empty rational Korselt sets
N Ghanmi
Hacettepe Journal of Mathematics and Statistics, 1-12 , 2022
2022
A novel decision making technique based on spherical hesitant fuzzy Yager aggregation information: application to treat Parkinson’s disease
M Naeem, A Khan, S Ashraf, S Abdullah, M Ayaz, N Ghanmi
AIMS Math 7 (2), 1678-1706 , 2022
2022
Citations: 11
Novel Analysis of Fractional‐Order Fifth‐Order Korteweg–de Vries Equations
AB Khoshaim, M Naeem, A Akgul, N Ghanmi, S Zaland
Journal of Mathematics 2022 (1), 1883268 , 2022
2022
Citations: 2
Intuitionistic fuzzy rough TOPSIS method for robot selection using Einstein operators
A Qadir, M Naeem, S Abdullah, N Ghanmi
2021
Citations: 8
Connections on the Rational Korselt Set of
N Ghanmi
Hacettepe Journal of Mathematics and Statistics, 1-9 , 2021
2021
The -Korselt set of
N Ghanmi
Periodica Mathematica Hungarica, 1-20 , 2020
2020
Citations: 2
Korselt rational bases of prime powers
N Ghanmi
Studia Scientiarum Mathematicarum Hungarica 56 (4), 388-403 , 2019
2019
Citations: 6
Korselt Rational Bases and Sets
N Ghanmi
arXiv preprint arXiv:1911.09324 , 2019
2019
On the Diophantine equation
N Ghanmi, FSA Muriefah
The Ramanujan Journal, 1-9 , 2019
2019
Citations: 3
-Korselt numbers
N Ghanmi
Turkish Journal of Mathematics 42 (5), 2752-2762 , 2018
2018
Citations: 7
On Williams numbers with three prime factors
N Ghanmi, I Al-Rassasi
Missouri Journal of Mathematical Sciences 25, 134-152 , 2013
2013
Citations: 6
On the korselt set of a squarefree composite number
I Al-Rasasi, O Echi, N Ghanmi
CR Math. Rep. Acad. Sci. Canada 35 (1), 1-15 , 2013
2013
Citations: 8
The Korselt set of
O Echi, N Ghanmi
International Journal of Number Theory 8 (02), 299-309 , 2012
2012
Citations: 15

MOST CITED SCHOLAR PUBLICATIONS

The Korselt set of
O Echi, N Ghanmi
International Journal of Number Theory 8 (02), 299-309 , 2012
2012
Citations: 15
A novel decision making technique based on spherical hesitant fuzzy Yager aggregation information: application to treat Parkinson’s disease
M Naeem, A Khan, S Ashraf, S Abdullah, M Ayaz, N Ghanmi
AIMS Math 7 (2), 1678-1706 , 2022
2022
Citations: 11
Intuitionistic fuzzy rough TOPSIS method for robot selection using Einstein operators
A Qadir, M Naeem, S Abdullah, N Ghanmi
2021
Citations: 8
On the korselt set of a squarefree composite number
I Al-Rasasi, O Echi, N Ghanmi
CR Math. Rep. Acad. Sci. Canada 35 (1), 1-15 , 2013
2013
Citations: 8
-Korselt numbers
N Ghanmi
Turkish Journal of Mathematics 42 (5), 2752-2762 , 2018
2018
Citations: 7
Korselt rational bases of prime powers
N Ghanmi
Studia Scientiarum Mathematicarum Hungarica 56 (4), 388-403 , 2019
2019
Citations: 6
On Williams numbers with three prime factors
N Ghanmi, I Al-Rassasi
Missouri Journal of Mathematical Sciences 25, 134-152 , 2013
2013
Citations: 6
On the Diophantine equation
N Ghanmi, FSA Muriefah
The Ramanujan Journal, 1-9 , 2019
2019
Citations: 3
Novel Analysis of Fractional‐Order Fifth‐Order Korteweg–de Vries Equations
AB Khoshaim, M Naeem, A Akgul, N Ghanmi, S Zaland
Journal of Mathematics 2022 (1), 1883268 , 2022
2022
Citations: 2
The -Korselt set of
N Ghanmi
Periodica Mathematica Hungarica, 1-20 , 2020
2020
Citations: 2
Research Article Novel Analysis of Fractional-Order Fifth-Order Korteweg–de Vries Equations
AB Khoshaim, M Naeem, A Akgul, N Ghanmi, S Zaland
2022
Numbers with empty rational Korselt sets
N Ghanmi
Hacettepe Journal of Mathematics and Statistics, 1-12 , 2022
2022
Connections on the Rational Korselt Set of
N Ghanmi
Hacettepe Journal of Mathematics and Statistics, 1-9 , 2021
2021
Korselt Rational Bases and Sets
N Ghanmi
arXiv preprint arXiv:1911.09324 , 2019
2019

Publications

1) Nejib Ghanmi and Othman Echi, The Korselt Set of pq, International Journal of
Number Theory Vol.8, No2 (2012) 299–309.

2) Nejib Ghanmi, Othman Echi and Ibrahim Al-Rassasi, The Korselt Set of a Square free Composite Number, of the Canadian Academy of Sciences, Vol 35, No1, (2013) 1-15.

3) Nejib Ghanmi and Ibrahim Al-Rassasi, On Williams Numbers With Three Prime
Factors, Missouri Journal of Mathematical Sciences, Vol 25, No 2, (2013) 134-152.

4) Nejib Ghanmi, Q-Korselt Numbers, Turk. J. Math 42(2018), 2752 - 2762.
5) Nejib Ghanmi, and Fadwa Abumuriefah, On Diophantine Equation Cx^2+D=2y^q , Ramanjuan journal.

6) Nejib Ghanmi, Korselt Rational bases of Prime Powers (in press).

7) Nejib Ghanmi, The Q-Korselt Set of pq (in press).

8) Connections on the Rational Korselt Set of pq (preprint)

9) Korselt Rational Bases and Sets (preprint)