Results 131 to 140 of about 92,931 (194)
Some of the next articles are maybe not open access.
Solutions for a Class of the Exponential Diophantine Equation
Advanced Materials Research, 2013We studied the Diophantine equation x2+4n=y11. By using the elementary method and algebraic number theory, we obtain the following conclusions: (i) Let x be an odd number, one necessary condition which the equation has integer solutions is that 210n-1/11 contains some square factors.
exaly +4 more sources
ON THE SOLUTION OF A CLASS OF EXPONENTIAL DIOPHANTINE EQUATIONS
South East Asian J. of Mathematics and Mathematical Sciences, 2022In this note, we show that for n = 4N + 3, N N 0 , the expo- nential Diophantine equation nx + 24y = z2 has exactly two solutions if n + 1 or equivalently N + 1 is an square. When N + 1 = m2, the solutions are given by (0, 1, 5) and (1, 0, 2m). Otherwise it has a unique solution (0, 1, 5) in non-negative integers.
Dutta, Mridul, Borah, Padma Bhushan
openaire +2 more sources
On the Exponential Diophantine Equation 27^x – 11^y = z^2
Journal of Physical Science, 2023In this article, we study and establish the theorem of the exponential Diophantine equation 27^x -11^y = z^2 , which has exactly two solutions where x, y and z are non-negative integers using Catalan’s conjecture, modular arithmetic, factorial method and
Rathindra Chandra Gope
semanticscholar +1 more source
An Exponential Diophantine Equation: 10873
The American Mathematical Monthly, 2003Solution by Doyle Henderson, Omaha, NE. The only possibilities for m are 0, 1, 2, 3, and 5. Simple calculations then show the solution set for (m, n) to be {(0, 0), (1, 1), (2, 2), (5, 11)1}. Suppose there is a solution with m even and at least 4. Let m = 2a and x = 3a We have x2 2n2 = 1.
B. J. Venkatachala, Doyle Henderson
openaire +2 more sources
ON THE EXPONENTIAL DIOPHANTINE EQUATION
Bulletin of the Australian Mathematical Society, 2014AbstractLet$m$,$a$,$c$be positive integers with$a\equiv 3, 5~({\rm mod} \hspace{0.334em} 8)$. We show that when$1+ c= {a}^{2} $, the exponential Diophantine equation$\mathop{({m}^{2} + 1)}\nolimits ^{x} + \mathop{(c{m}^{2} - 1)}\nolimits ^{y} = \mathop{(am)}\nolimits ^{z} $has only the positive integer solution$(x, y, z)= (1, 1, 2)$under the condition ...
TAKAFUMI MIYAZAKI, NOBUHIRO TERAI
openaire +1 more source
European Journal of Pure and Applied Mathematics
We prove that the exponential Diophantine equation \( 23^x + 22^y = z^2 \) has no nonnegative integer solutions. Using a combination of modular arithmetic, parity analysis, and computational verification, we demonstrate that the equation leads to ...
A. Assiry
semanticscholar +1 more source
We prove that the exponential Diophantine equation \( 23^x + 22^y = z^2 \) has no nonnegative integer solutions. Using a combination of modular arithmetic, parity analysis, and computational verification, we demonstrate that the equation leads to ...
A. Assiry
semanticscholar +1 more source
The Search for Non-Negative Integer Solutions to Exponential Diophantine Equation
International Journal for Research in Applied Science and Engineering TechnologyIn this manuscript, an exponential Diophantine equation 〖(3λ^2+5)〗^x+〖(6λ^2+11)〗^y=μ^2,for some selected choices of non-negative integers and λ ,μ∈Z is scrutinized for all the amalgamation ofx +y = 1,2,3 and proved that the essentialsolutions are (x,y,λ ...
B. Umamaheswari, V. Pandichelvi
semanticscholar +1 more source
Annals of Pure and Applied Mathematics
Let 𝑘, 𝑥, 𝑦, and 𝑧 be non-negative integers. Consider the Exponential Diophantine equation (3 k - 1) x + (3 k ) y = z 2 . This is a non-linear Diophantine equation in four variables 𝑘, 𝑥, 𝑦 and 𝑧.
Chikkavarapu Gnanendra Rao
semanticscholar +1 more source
Let 𝑘, 𝑥, 𝑦, and 𝑧 be non-negative integers. Consider the Exponential Diophantine equation (3 k - 1) x + (3 k ) y = z 2 . This is a non-linear Diophantine equation in four variables 𝑘, 𝑥, 𝑦 and 𝑧.
Chikkavarapu Gnanendra Rao
semanticscholar +1 more source
MATRIX SOLUTIONS FOR THE NON-LINEAR EXPONENTIAL DIOPHANTINE EQUATION
JP Journal of Algebra Number Theory and ApplicationsWe investigate matrix solutions for the non-linear exponential Diophantine equation where and such that is a common multiple of and . We show that this equation admits an infinite number of matrix solutions which do not depend on and .
Kolo F. Soro
semanticscholar +1 more source
On the exponential Diophantine equation 37^x-5^y = z^2
International Journal of Mathematical and Computer SciencesIn this paper, we show that (0, 0, 0) and (1, 0, 6) are the only two non-negative integer solutions of the exponential Diophantine equation 37^x-5^y = z^2.
H. Tansee, C. Namnak
semanticscholar +1 more source