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Issue 1 − C
Volume 4 (2016)

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Article Type |
: | Research Article |

Title |
: | I-Convergence Difference Sequence Classes of Fuzzy Real Numbers Defined By Sequence of Modulus Functions |

Country |
: | India |

Authors |
: | Manmohan Das || Sanjay Kr. Das |

**Abstract: ** In this article our aim to introduce some new I- convergence difference sequence classes of fuzzy real numbers defined by sequence of modulus functions and studies some topological and algebraic properties. Also we establish some inclusion relations.

**Keywords: ** Fuzzy real number, I- convergence, modulus function, difference sequence.

Manmohan Das

Department of Mathematics, Bajali College (Gauhati University), Assam, India.

E-mail: mdas.bajali@gmail.com

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Article Type |
: | Research Article |

Title |
: | Soft Pre Generalized Closed Sets With Respect to a Soft Ideal in Soft Topological Spaces |

Country |
: | India |

Authors |
: | V.Chitra || V.Inthumathi || K.Nirmaladevi |

**Abstract: ** In this paper, we extend the concept of soft pre generelized closed sets due to J. Subhashini and C. Sekar [15] to soft pre generalized closed sets with respect to a soft ideal and study some of their basic properties.

**Keywords: ** Soft sets, Soft topological spaces, Soft pg-closed set, soft g-closed set, Soft $I_g$-closed set and Soft $I_{pg}$-closed set.

K.Nirmaladevi

Department of Mathematics, Sri Krishna Arts and Science College, Coimbatore, Tamilnadu, India.

E-mail: nirmalamaths8@gmail.com

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Article Type |
: | Research Article |

Title |
: | On Relaxed Skolem Mean Labling For Four Star |

Country |
: | India |

Authors |
: | V.Balaji|| D.S.T.Ramesh || M.Elakkiya |

**Abstract: ** In this paper, we prove that if $\ell $= m $<$ n, the four star K${}_{1, }$${}_{\ell }$${}_{ }$$\cup$ K${}_{1, }$${}_{\ell }$${}_{ }$$\cup$ K${}_{1, m }$$\cup$ K${}_{1, n}$ is a relaxed skolem mean graph if $|m-n|\, \le \, 2\ell \, +6$ for $\ell $= 2, 3, 4, . . . ; m = 2, 3, 4, . . . and $2\ell +m\, \le n\, \le \, 2\ell \, +\, m\, +6$.

**Keywords: ** Skolem mean graph and star.

V.Balaji

Department of Mathematics, Sacred Heart College, Tirupattur, India.

E-mail: pulibala70@gmail.com

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Article Type |
: | Research Article |

Title |
: | Some Types of Generalized $H^h$-Recurrent in Finsler Spaces |

Country |
: | Yemen |

Authors |
: | Fahmi Yaseen Abdo Qasem || Adel Mohammed Ali AL-Qashbari |

**Abstract: ** The purpose of this paper is to develop some
properties of generalized $H^{h}$-recurrent affinely connected
space, P2-like generalized $H^{h}$-recurrent space and $P^{\ast}$-generalized $H^{h}$-recurrent space for Berwald curvature tensor $H_{jkh}^{i}$ which satisfies the condition $H_{jkh\vert l}^{i}=\lambda_{l}H_{jkh}^{i}+\mu_{l}(\delta _{h}^{i} g_{jk}-\delta_{k}^{i} g_{jh})$, where $\vert l$ is h-covariant differentiation, $\lambda_{l}$ and $\mu_{l}$ are non-null covariant vectors field
is introduced and such space is called as a generalized $H^{h}$-recurrent space and denote it briefly by
$G H^{h}$-$R F_{n}$.
Some theorems and conditions have been pointed out which reduce a generalized $H^{h}$-recurrent space $F_{n}(n>2)$ into a Finsler space of curvature scalar.

**Keywords: ** Finsler space, Generalized H-recurrent space, affinely connected space, P2-like space and $P^{\ast}$-space.

Adel Mohammed Ali AL-Qashbari

Department of Mathematics, Faculty of Education, University of Aden, Khomaksar, Aden, Yemen.

E-mail: Adel_ma71@yahoo.com

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Article Type |
: | Research Article |

Title |
: | On a Generalized K^h- Birecurrent Finsler Space |

Country |
: | Yemen |

Authors |
: | Fahmi Yaseen Abdo Qasem || Wafa'a Hadi Ali Hadi |

**Abstract: ** In the present paper, a Finsler space whose curvature tensor $K^i_{jkh}$ satisfies $K^i_{jkhÐ\ell Ðm}{\rm =\ }{\ a}_{\ell m}K^i_{jkh}+{\ b}_{\ell m}\left({\delta }^i_kg_{jh}-{\delta }^i_hg_{jk}\right)\ ,K^i_{jkh}\ne $ 0 , where ${\ a}_{\ell m}$ and ${\ b}_{\ell m}\ $are non-zero covariant tensor fields of second order called recurrence tensor fields, is introduced, such space is called as a generalized $K^h-$birecurrent Finsler space . The associate tensor $K_{jrkh}$ of Cartan's fourth curvature tensor $K^i_{jkh}$ , the torsion tensor $H^i_{kh}$ ,the deviation tensor $K^i_h$, the Ricci tensor $K_{jk}$, the vector $H_k$ and the scalar curvature $K$ of such space are non-vanishing. Under certain conditions, a generalized $K^h-$birecurrent Finsler space becomes Landsberg space .
Some conditions have been pointed out which reduce a generalized $K^h-$birecurrent Finsler space $F_n(n>2)$ into Finsler space of scalar curvature.

**Keywords: ** Finsler space; Generalized K^h-birecurrent Finsler space; Ricci tensor; Landsberg space; Finsler space of scalar curvature.

Wafa'a Hadi Ali Hadi

Department of Mathematics , Community College-Aden, Dar Saad , Aden, Yemen.

E-mail: wf_hadi@yahoo.com

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Article Type |
: | Research Article |

Title |
: | Some Results for Semi Derivations of Prime Near Rings |

Country |
: | India |

Authors |
: | Meram Munirathnam |

**Abstract: ** Let $R$ be a prime near ring. By a semi-derivation associated with a function $g:R \rightarrow R$ we mean an additive mapping $f: R \rightarrow R$ such that $ f (xy) =f (x)g(y) + xf (y) = f (x)y + g(x)f (y)$ and $f (g(x)) = g(f (x)) $ for all $x, y \in R$. In this paper we try to generalize some properties of prime rings with derivations to the prime near rings with semi-derivations.

**Keywords: ** Semi derivation, Prime ring, Commuting mapping, Characteristic of a ring.

Meram Munirathnam

Ad-hoc Lecturer, Dept. of Mathematics, RGUKT, R.K.Valley, Idupulapaya(vi),Vempalli (md), Kadapa(Dt), Andhra Pradesh, India.

E-mail: munirathnam1986@gmail.com

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Article Type |
: | Research Article |

Title |
: | Some Unified and Generalized Kummer's Second Summation Theorems with Applications in Laplace Transform Technique |

Country |
: | India |

Authors |
: | M.I.Qureshi || M.S.Baboo |

**Abstract: ** Some significant hypergeometric summation theorems with suitable convergence conditions, are obtained in the present study; analogous to summation theorems for Gauss function ${_2F_1(\frac{1}{2})}$ presented by Brychkov, Prudnikov {\it et~al.} and derived by Fox, Rakha-Rathie. By means of these summation theorems we also find the Laplace transforms of Kummer's confluent hypergeometric function $_1F_1$ in closed form.

**Keywords: ** Gauss and Kummer hypergeometric functions; Legendre duplication formula; Pfaff-Kummer's linear hypergeometric transformation; Principle of analytic continuation; Laplace transforms.

M.S.Baboo

School of Basic Sciences and Research, Sharda University, Greater Noida, Uttar Pradesh, 201306, India.

E-mail: mesub007@gmail.com

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Article Type |
: | Research Article |

Title |
: | Ciric Type Coincidence and Fixed Point Results For Nonexpansive Multi-Valued and Single Valued Maps |

Country |
: | India |

Authors |
: | Umesh Dongre || R.D.Daheriya || Manoj Ughade |

**Abstract: ** In this paper we consider the existence of coincidences and fixed points of nonexpansive type conditions satisfied by multivalued and single valued maps and prove some fixed point theorems for nonexpansive type single and multivalued mappings.

**Keywords: ** Coincidence point; fixed point; non-expansive mappings; compatible mappings; T-orbitally complete; (T, f)-orbitally complete.

Manoj Ughade

Department of Mathematics, Sarvepalli Radhakrishnan University, Bhopal, P.O. Box 462026, India.

E-mail: surajshrivastava70@gmail.com

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Article Type |
: | Research Article |

Title |
: | Balanced Cordial Labeling and its Application to Produce new Cordial Families |

Country |
: | India |

Authors |
: | V.J.Kaneria || K.M.Patadiya || J.R.Teraiya |

**Abstract: ** In this paper we have introduced a balanced cordial labeling for a graph G, which is a cordial labeling $ f $ with condition $ e_{f}(0)= e_{f}(1), v_{f}(0)= v_{f}(1). $ We proved that $ P_{n} \times C_{4t}, C_{n} \times C_{4t}$ ($n$ is even) are balanced cordial graphs. We also proved that the corona graph $ G_{1} \odot G_{2} $ is cordial, when $ G_{1} $ a cordial graph and $ G_{2} $ is a balanced cordial graph.

**Keywords: ** Binary vertex labeling, balanced cordial graph, corona graph.

K.M.Patadiya

School of Engineering, RK University, Rajkot, India.

E-mail: kalpesh.patadiya$@$rku.ac.in

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Article Type |
: | Research Article |

Title |
: | The Edge Zagreb indices of Circumcoronene Series of Benzenoid |

Country |
: | Iran |

Authors |
: | M.R.Farahani || M.R.Rajesh Kanna || R.Pradeep Kumar || S.Hosamani |

**Abstract: ** In chemical graph theory, we have many
invariant polynomials and topological indices for a molecular
graph. One of the best known and widely used is the Zagreb
topological index of a graph $G$ $M_1(G)$ introduced in 1972 by
I. Gutman and N. Trinajstic and is defined as the sum
of the squares of the degrees of all vertices of $G$,
$M_{1}(G)=\sum\limits_{v\in V(G)} {d_{v}}^2$ (or $=\sum\limits_{e=uv\in E(G)}
{d_{u}+d_{v}}$, where $d_{u}$ denotes the degree (number of first
neighbors) of vertex $u$ in $G$. Also, the Second Zagreb index
$M_2(G)$ is equal to $M_{2}(G)=\sum\limits_{e=uv\in E(G)} {d_{u} \times
d_{v}}$. In this paper, we focus on the structure of molecular
graph Circumcoronene Series of Benzenoid $H_{k}$ ($k>1$)
and its line graph $L(H_{k})$ and counting First Zagreb index and
Second Zagreb index of $L(H_{k})$.

**Keywords: ** Circumcoronene Series of Benzenoid, Line graph, Degree (of a vertex), Zagreb Topological Index.

M.R.Farahani

Department of Applied Mathematics of Iran University of Science and Technology (IUST), Narmak, Tehran, Iran.

E-mail: mrfarahani88@gmail.com

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Article Type |
: | Research Article |

Title |
: | Some Common Fixed Point Theorems For Nonexpansive Type Mappings In 2-Metric Spaces |

Country |
: | India |

Authors |
: | Ritu Sahu || P L Sanodia || Arvind Gupta |

**Abstract: ** The aim of this paper is to prove some common fixed point theorems for weakly compatible mappings under nonexpansive type conditions in the setting of 2-metric spaces. Our result extend and generalizes corresponding results of Singh, Adiga and Giniswami [9] and Liu and Zhang [7].

**Keywords: ** 2-metric spaces, nonexpansive mapping,compatible mappings compatible mapping of type (A).

Ritu Sahu

Department of Mathematics, People’s College of Research & Technology, Bhopal, India

E-mail: sahuritu00@gmail.com

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Article Type |
: | Research Article |

Title |
: | A New Approach For Solving All Integer Linear Fractional Programming Problem |

Country |
: | India |

Authors |
: | Geeta Modi || Sushma Duraphe || Huma Akhtar |

**Abstract: ** In this paper we present a new approach for solving all
integer linear fractional programming problem (ILFPP) in which the objective function is a linear fractional function,
and where the constraint functions are in the form of linear inequalities. The approach adopted is based mainly upon
simplex method as well as dual simplex method. A simple example is given to clarify the theory of this new approach.

**Keywords: ** Fractional programming, Simplex method, Dual simplex method, Gomory’s fractional cut method.

Huma Akhtar

Research Scholar, Govt. M.V.M. Bhopal, India.

E-mail: akhtarhuma50@gmail.com

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Article Type |
: | Research Article |

Title |
: | Key mortality factors of Scirpophaga incertulas (Rice stem borer) infesting Rice |

Country |
: | India |

Authors |
: | S.Udayakumar || P.Sujatha || P.Yasotha |

**Abstract: ** Scirpophagaincertulaspassed through one generation each during rainy season at Agricultural Engineering College, Kumulur. TrichogrammaJaponicum,Trichogrammabraziliensis, Telenomusbeneficiens, Tetra stichus SP. are egg parasites and BraconChinensis, Stenobraconnicenilles, Tropobracon sp. Platygaster. In addition to the above TrichogrammaJaponicum and playgasterOryzac unidentified as key mortality factors of scirpopherga incertulas. Using the key mortality factors the killing power of k value is decrease by second generation.

**Keywords: ** Rice, Key Mortality factors, Scirpophaga incertulas.

P.Sujatha

Assistant Professor(Maths), Ph.D Research Scholar, Horticultural college and Research Institute (women), Tamil Nadu Agricultural University, Trichy, India.

E-mail:

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Article Type |
: | Research Article |

Title |
: | Super Root Square Mean Labeling Of Disconnected Graphs |

Country |
: | India |

Authors |
: | M.Kannan || R.Vikrama Prasad || R.Gopi |

**Abstract: ** Let G be a graph with p vertices and q edges. Let $f:V(G)\to \{1, 2, 3,\dots, p+q\} be an
injective function. For a vertex labeling f, the induced edge labeling $f^\ast(e=uv)$ is defined by then f is called a super root square mean if .
A graph which admits super root square mean labeling is called super root square mean graph. In this paper, we investigate super root square mean
labeling of disconnected graphs.

**Keywords: ** Super root square mean,

M.Kannan

Research & Development Centre, Bharathiar University, Coimbatore – 641 046, India.

E-mail: kannan8383@gmail.com

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Article Type |
: | Research Article |

Title |
: | Asymptotic Stability In Impulsive Functional Differential Equations |

Country |
: | India |

Authors |
: | Sanjay K. Srivastava || Neha Wadhwa || Neeti Bhandari |

**Abstract: ** In this paper conditions on Lyapunov functionals $V(t, \phi)$ are improved
which ensure asymptotic stability and uniform asymptotic stability.

**Keywords: ** Stability, Asymptotic Stability, Impulsive Functional Differential Equation, Lyapunov functional.

Neha Wadhwa

Department of Applied Sciences, Amritsar College of Engineering and Technology, Amritsar - 143006, Punjab, India.

E-mail: nehawadhwa08@yahoo.com

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Article Type |
: | Research Article |

Title |
: | Construction of Two Special Integer Triples |

Country |
: | India |

Authors |
: | S.Vidhyalakshmi || M.A.Gopalan || E.Premalatha |

**Abstract: ** This paper concerns with the study of constructing a special non zero integer triple (a, b, c) such that the product of any two elements of the set added with the other is a perfect square. Also, the product of any two elements of the set added with the square of the other is a perfect square.

**Keywords: ** Integer Triple, system of double equation

E.Premalatha

Department of Mathematics, National College, Trichy, Tamil Nadu, India.

E-mail: premalathaem@gmail.com

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Article Type |
: | Research Article |

Title |
: | Parametric Metric Space, Parametric b-metric Space and Expansive Type Mapping |

Country |
: | India |

Authors |
: | R.D.Daheriya || Suraj Shrivastava || Manoj Ughade |

**Abstract: ** In this article, we present some fixed point theorems under various expansive conditions in parametric metric spaces and parametric b-metric spaces. The presented theorems extend, generalize and improve many existing results in \cite{13}. Also we prove a common fixed point theorem, which is generalization of Theorem 2.2 of Jain et al. \cite{24} in the setting of parametric b-metric space. We introduce an example the support the validity of our result.

**Keywords: ** Fixed point, common fixed point, parametric metric space, parametric b-metric space.

Suraj Shrivastava

Department of Mathematics, Swami Vivekanand College of Science and Technology, Bhopal, Madhya Pradesh, India.

E-mail: surajshrivastava70@gmail.com

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Article Type |
: | Research Article |

Title |
: | Obscuring Instability In C Language Using Euler's Modified Method |

Country |
: | India |

Authors |
: | Sonia Shivhare || Yogesh Shukla |

**Abstract: ** The solutions of ordinary Differential equations having initial value problems are analyzed numerically. Computationally effective numerical methods, Euler’s method is given meticulously while Euler’s Modified method presented here gives a better exactness. No higher order derivatives are required to be tabulated. Drawbacks and advantages of the methods are discussed here and the results obtained by them have been compared. The idea behind this paper is to illustrate the facts of implementing a small number of steps of Euler's modified method, in addition , how to apply built-in functions available in C++ [1]. Firstly, we use Euler methods to bring in the fundamental thoughts linked with initial value problems (IVP) and then later on, we apply the Euler’s Modified method associated to the built-in C++ . The purpose of this paper is to go from textbook formula on ODE to production software.

**Keywords: ** Euler’s Method, Euler’s Modified Method, C++, ODE.

Yogesh Shukla

Amity University, Madhya Pradesh, India.

E-mail:

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Article Type |
: | Research Article |

Title |
: | Lucky Edge Labeling of $K_n$ and Special Types of Graphs |

Country |
: | India |

Authors |
: | R.Sridevi || S.Ragavi |

**Abstract: ** Let G be a simple graph with vertex set V(G) and edge set E(G) respectively. Vertex set V(G) is labeled arbitrary by positive integers and E(e) denote the edge label such that it is the sum of labels of vertices incident with edge e. The labeling is said to be lucky edge labeling if the edge E(G) is a proper coloring of G, that is, if we have $E(e_{1})\neq E(e_{2})$ whenever $e_{1}$ and $e_{2}$ are adjacent edges. The least integer k for which a graph G has a lucky edge labeling from the set $\{1, 2,\dots, k\}$ is the lucky number of G denoted by $\eta(G)$. A graph which admits lucky edge labeling is the lucky edge labeled graph. In this paper, we proved that complete graph $K_{n}$, tadpole graph $T_{m, n}$ and rectangular book $B_{p}^{4}$ are lucky edge labeled graphs.

**Keywords: ** Lucky edge labeled graph, Lucky edge labeling, Lucky number.

S.Ragavi

Research Scholar, Department of Mathematics, Sri S.R.N.M.College, Sattur, Tamilnadu, India.

E-mail: stragavi22@gmail.com

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Article Type |
: | Research Article |

Title |
: | Finite Product Topologies Modulo An Ideals |

Country |
: | India |

Authors |
: | R.Alagar |

**Abstract: ** Given a topological space (X,$\tau $) and an ideal$\Im $ in X, a
finer topology $\tau $* in X can be associated with $\tau $ and$\Im $. Given two topological
spaces (X,$\tau $${}_{1}$), (Y,$\tau $${}_{2}$) and ideals $\Im $, $\vartheta$ in X, Y respectively,
an ideal $\Im $x $\vartheta$ in X x Y, called the product ideal of $\Im $and $\vartheta$, in X x Y.
We investigate inclusion relations between $\tau $${}_{1}$* x $\tau $${}_{2}$* and
($\tau $${}_{1}$ x $\tau $${}_{2 }$)* and the conditions under which $\tau $${}_{1}$* x $\tau $${}_{2}$* = ($\tau $${}_{1}$ x $\tau $${}_{2 }$)* and
we extend the theorem for finite case.

**Keywords: ** Product ideal, Product Topology,$\tau $* - topologies, $\pi \tau _{\alpha } $* - closed.

R. Alagar

Department of Mathematics, R.V. Government Arts college, Chengalpattu – 603 001.

E-mail:

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Article Type |
: | Research Article |

Title |
: | Regular And Totally Regular Intuitionistic Fuzzy Hypergraph(IFH) |

Country |
: | India |

Authors |
: | I.Pradeepa || S.Vimala |

**Abstract: ** Regular and totally regular Intuitionistic fuzzy
graph was first introduced by Nagoor gani.A and Radha.K. In this paper, we define regular and totally regular
Intuitionistic fuzzy hypergraphs and discusses the size and order along with properties of the regular and totally
regular Intuitionistic fuzzy hypergraphs. The work has been extended to completeness of Intuitionistic fuzzy hypergraphs.

**Keywords: ** Intuitionistic fuzzy graph, Regular intuitionistic fuzzy graph,Totally Regular intuitionistic fuzzy graph,Degree,Total degree.

I.Pradeepa

Assistant Professor, Department of Mathematics, Mother Teresa Women’s University, Kodaikanal, India.

E-mail: tvimss@gmail.com

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Article Type |
: | Research Article |

Title |
: | Adjacent vertex sum polynomial for the splitting graph of Factographs |

Country |
: | India |

Authors |
: | E.Ebin Raja Merly || A.M.Anto |

**Abstract: ** Let $G=(V, E)$ be a graph. The vertex polynomial of the graph $G=(V,E)
$ is defined as $V(G,x)=\sum\limits_{k=0}^{\Delta(G)}{v_{k}x^{k}}$, where $\Delta (G)=\max\{d(v)/v\in V\}$ and $v_{k}$ is the number of
vertices of degree $k$. The adjacent vertex sum polynomial is defined
as $S(G, x)=\sum\limits_{i=o}^{\Delta(G)}{n_{\Delta(G)-i}x^{\alpha_{\Delta
(G)-i}}}$, where $n_{\Delta(G)-i}$ is the sum of the number of
adjacent vertices of all the vertices of degree $\Delta(G)-i$ and $\alpha_{\Delta(G)-i}$ is the sum of the degree of adjacent vertices
of all the vertices of degree $\Delta(G)-i$. In this paper we seek
to find the vertex polynomial and the adjacent vertex sum polynomial for
the splitting graph of Perfect factograph and the splitting graph of
Integral Perfect factograph.

**Keywords: ** Perfect factograph, Integral Perfect factograph, Vertex polynomial, Adjacent vertex sum polynomial, Splitting graph.

A.M.Anto

Research scholar, Department of Mathematics, Nesamony Memorial Christian College, Marthandam, India.

E-mail: antoalexam@gmail.com

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Article Type |
: | Research Article |

Title |
: | Prime number generating polynomial $3n^2+3n+23$ |

Country |
: | India |

Authors |
: | Jeevan Maloth |

**Abstract: ** A prime number is positive integer which does not divisible by any integers except 1 and
itself. Up to now there is no any polynomial which generates all primes. There are few polynomial generate finite primes. In this paper I am giving a new polynomial
which generating prime numbers from n= 0 to 21.

**Keywords:** Prime-generating polynomial.

Jeevan Maloth

Student of the Electrical Department, St. Martin’s Engineering College,
Dhulapally, Secunderabad, Telangana, India.

E-mail: jeevannayak777@gmail.com