Results 41 to 50 of about 2,597 (231)

Bound on some Diophantine equation [PDF]

, 2022
Diophantine equation is known as a polynomial equation with two or more unknowns which only integral solutions are sought. This paper will concentrate on finding the least upper bound to the Diophantine equation x 2 + 2a 7 b = y n for 1 ≤ α ≤ 8 and found
Amalulhair, N. H., Sapar, S. H., Johari, M. A. M.   +2 more
core  

On simultaneous diophantine equations [PDF]

Acta Arithmetica, 2003
The authors investigate the number of solutions of the simultaneous Diophantine equations \[ x^2- (M^2+4)y^2= -4, \quad y^2-dz^2=1, \tag{1} \] where \(M\) is assumed to be an odd positive integer and where \(d\) is a squarefree integer. They show that for squarefree \(d\) with at most four distinct prime factors, system (1) can have at most one ...
Katayama, Shin-ichi, Levesque, Claude
openaire   +1 more source

NOTE ON THE DIOPHANTINE EQUATION [PDF]

, 2000
NOTE ON THE DIOPHANTINE ...
Atanassov, Krassimir, Atanassov, Missana, Vassilev, Mladen V.   +2 more
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ON SOLVING A QUADRATIC DIOPHANTINE EQUATION [PDF]

, 2022
Diophantine Equations named after ancient Greek mathematician Diophantus, plays a vital role not only in number theory but also in several branches of science.
Dr. R. Sivaraman
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A brief survey on the generalized Lebesgue-Ramanujan-Nagell equation [PDF]

Surveys in Mathematics and its Applications, 2020
The generalized Lebesgue-Ramanujan-Nagell equation is an important type of polynomial-exponential Diophantine equation in number theory. In this survey, the recent results and some unsolved problems of this equation are given.
Maohua Le, Gökhan Soydan
doaj  

On a quartic diophantine equation [PDF]

, 1996
In this paper we consider the quartic diophantine equation 3(y2 – 1) = 2x2(x2 – 1) in integers x and y. We show that this equation does not have any other solutions (x, y) with x¿0 than those given by x = 0,1,2,3,6,91.
Weger, de, B.M.M., de Weger, BMM (Frederike), Stroeker, RJ (Roel), Stroeker, R.J.   +3 more
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On the Symbolic 2-plithogenic Fermat's Non-Linear Diophantine Equation [PDF]

Neutrosophic Sets and Systems, 2023
This paper is dedicated to find all symbolic 2-plithogenic integer solutions for the symbolic 2-plithogenic Fermat's Diophantine equation.
Heba Alrawashdeh, Othman Al-Basheer, Arwa Hajjari   +2 more
doaj  

On 1w+1x+1y+1z=12 $\frac{1}{w} + \frac{1}{x} + \frac{1}{y} + \frac{1}{z} = \frac{1}{ 2} $ and some of its generalizations

Journal of Inequalities and Applications, 2018
In this paper, we give a straightforward approach to obtaining the solution of the Diophantine equation 1w+1x+1y+1z=12 $\frac{1}{w} + \frac{1}{x} + \frac{1}{y} + \frac{1}{z} = \frac{1}{2}$. We also establish that the Diophantine equation 1w+1x+1y+1z=mn $\
Tingting Bai
doaj   +1 more source

On a class of diophantine equations [PDF]

International Journal of Mathematics and Mathematical Sciences, 2002
Cohn (1971) has shown that the only solution in positive integers of the equation Y(Y + 1)(Y + 2)(Y + 3) = 2X(X + 1)(X + 2)(X + 3) is X = 4, Y = 5. Using this result, Jeyaratnam (1975) has shown that the equation Y(Y + m)(Y + 2m)(Y + 3m) = 2X(X + m)(X + 2m)(X + 3m) has only four pairs of nontrivial solutions in integers given by X = 4m or −7m, Y = 5m ...
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Studies of Positive Integer Solutions of the Diophantine Equation x2−ay2−bx−cy−d=0 by the Transformation Method

Journal of Mathematics
Solving the Diophantine equation has fascinated mathematicians from various civilizations. In this paper, we propose the resolution of quadratic Diophantine equations with integer coefficients.
Francklin Fenolahy, Harrimann Ramanantsoa, André Totohasina   +2 more
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