Results 41 to 50 of about 2,595 (231)

Diophantine Equation in Logarithms

, 2023
The main work of these pages is written by myself under the supervisor of Dr. Omar Kihel, pertaining to continued fractions and applications , linear form in logarithms and the solutions of Diophantine equation Fn1 + Fn2 + Fn3 + Fn4 = 6a .
Tian, Zhao
core  

Cryptography Using Linear Diophantine Equation

, 2022
: This study is focused on the encrypting and decrypting of messages using the Linear Diophantine Equation: where , that is the integers and are relatively prime.
Mark Kenneth C. Engcot
core   +1 more source

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 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 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 ...
openaire   +3 more sources

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
doaj   +1 more source

Random Diophantine equations in the primes

Mathematika, Volume 72, Issue 3, July 2026.
Abstract We consider equations of the form a1x1k+⋯+asxsk=0$a_{1}x_{1}^{k}+\cdots +a_{s}x_{s}^{k}=0$ where the variables xi$x_{i}$ are all taken to be primes. We define an analogue of the Hasse principle for solubility in the primes (which we call the prime Hasse principle), and prove that, whenever k⩾2$k\geqslant 2$, s⩾3k+2$s\geqslant 3k+2$, this holds
Philippa Holdridge
wiley   +1 more source

Three Diophantine equations concerning the polygonal numbers [PDF]

Notes on Number Theory and Discrete Mathematics
Many authors investigated the problem about the linear combination of two polygonal numbers being a perfect square, i.e., the Diophantine equation mPₖ(x)+nPₖ(y)=z², where Pₖ(x) denotes the x-th k-polygonal number and m, n are positive integers.
Yong Zhang, Mei Jiang, Qiongzhi Tang
doaj   +1 more source

Kripke on Gödel Incompleteness

Theoria, Volume 92, Issue 3, June 2026.
ABSTRACT This paper surveys six of Saul Kripke's highly creative ideas and results on Gödel incompleteness, from when he was an undergraduate to last publications. These include his extension of incompleteness from sentences to predicates, his model‐theoretic proof of incompleteness of arithmetic, his compelling analysis of incompleteness in terms of ...
Daniel Isaacson
wiley   +1 more source

On the Diophantine equation $x^2+2^\alpha 5^\beta 17^\gamma =y^n$

, 2012
summary:In this paper, we find all solutions of the Diophantine equation $x^2+2^\alpha 5^\beta 17^\gamma = y^n$ in positive integers $x,y\geq 1$, $\alpha ,\beta ,\gamma ,n\geq 3$ with $\gcd (x,y)=1$
Godinho, Hemar, Marques, Diego, Togbé, Alain   +2 more
core   +1 more source