Results 31 to 40 of about 92,931 (194)
On the Exponential Diophantine Equation 10x – 17y = z2
Annals of Pure and Applied Mathematics, 2023 . In this study, our aim is to prove all the solutions of the exponential Diophantine equation 10 x – 17 y = z 2 , where x, y and z are non-negative integers. We applied the modular arithmetic and Catalan’s conjecture to obtain all solutions.
W. Chuayjan, S. Thongnak, T. Kaewong
semanticscholar +1 more source
A Survey on the ternary purely exponential diophantine equation ax + by = cz [PDF]
Surveys in Mathematics and its Applications, 2019 Let a, b, c be fixed coprime positive integers with min(a,b,c)>1. In this survey, we consider some unsolved problems and related works concerning the positive integer solutions (x,y,z) of the ternary purely exponential diophantine equation ax + by = cz.
Maohua Le, Reese Scott, Robert Styer
doaj
An upper bound for solutions of the Lebesgue-Nagell equation x 2 + a 2 = y n $x^{2}+a^{2}=y^{n}$
Journal of Inequalities and Applications, 2016 Let a be a positive integer with a > 1 $a>1$ , and let ( x , y , n ) $(x, y, n)$ be a positive integer solution of the equation x 2 + a 2 = y n $x^{2}+a^{2}=y^{n}$ , gcd ( x , y ) = 1 $\gcd(x, y)=1$ , n > 2 $n>2$ .
Xiaowei Pan
doaj +1 more source
On the Exponential Diophantine Equation 3x - 5y = z2
Annals of Pure and Applied Mathematics, 2023 . In this study, we prove all solutions of the exponential Diophantine equation 3 x (cid:1) 5 y = z 2 where x, y and z are non-negative integers. The result indicates that the solutions ( x, y, z ) are (0, 0, 0) and (2, 1, 2).
W. Chuayjan, S. Thongnak, T. Kaewong
semanticscholar +1 more source
Exponential diophantine equations in rings of positive characteristic [PDF]
Journal of Knot Theory and Its Ramifications, 2020 In this paper, we prove an algorithmical solvability of exponential-Diophantine equations in rings represented by matrices over fields of positive characteristic. Consider the system of exponential-Diophantine equations [Formula: see text] where [Formula: see text] are constants from matrix ring of characteristic [Formula: see text], [Formula: see ...
Chilikov, A. A., Belov-Kanel, Alexey
openaire +1 more source
On the Diophantine equation 2x + 11y = z2 [PDF]
Maejo International Journal of Science and Technology, 2013 In this paper it is shown that (3,0,3) is the only non-negative integer solution of the Diophantine equation 2x + 11y = z2.
Somchit Chotchaisthit
doaj
Exponential Diophantine equations for correlation functions of the Tchebyscheff maps
四川大学学报. 自然科学版, 2023 Tchebyscheff maps are typical chaotic maps. Correlation functions play a key role in the study of their statistical properties. This paper aims at the solutions of a class of exponential Diophantine equations arising in the calculation of correlation ...
ZHOU Xing-Wang
doaj
Common values of two k-generalized Pell sequences [PDF]
Notes on Number Theory and Discrete MathematicsLet k≥2 and let (Pₙ⁽ᵏ⁾)ₙ≥₂₋ₖ be the k-generalized Pell sequence defined by Pₙ⁽ᵏ⁾=2Pₙ₋₁⁽ᵏ⁾+2Pₙ₋₂⁽ᵏ⁾+...+2Pₙ₋ₖ⁽ᵏ⁾ for n≥2 with initial conditions P₋₍ₖ₋₂₎⁽ᵏ⁾=P₋₍ₖ₋₃₎⁽ᵏ⁾=...=P₋₁⁽ᵏ⁾=P₀⁽ᵏ⁾=0, and P₁⁽ᵏ⁾=1.
Zafer Şiar +2 more
doaj +1 more source
On the Exponential Diophantine Equation $(6m^{2}+1)^{x}+(3m^{2}-1)^{y}=(3m)^{z}$
Fundamental Journal of Mathematics and Applications, 2022 Let $m$ be a positive integer. In this paper we consider the exponential Diophantine equation $(6m^{2}+1)^{x}+(3m^{2}-1)^{y}=(3m)^{z}$ and we show that it has only unique positive integer solution $(x,y,z)=(1,1,2)$ for all $ m>1.
M. Alan, Ruhsar Gizem Bi̇ratli
semanticscholar +1 more source
On a conjecture on exponential Diophantine equations [PDF]
Acta Arithmetica, 2009 We study the solutions of a Diophantine equation of the form $a^x+b^y=c^z$, where $a\equiv 2 \pmod 4$, $b\equiv 3 \pmod 4$ and $\gcd (a,b,c)=1$. The main result is that if there exists a solution $(x,y,z)=(2,2,r)$ with $r>1$ odd then this is the only solution in integers greater than 1, with the possible exception of finitely many values $(c,r)$. We
Cipu, Mihai, Mignotte, Maurice
openaire +2 more sources