Results 21 to 30 of about 321 (189)

On the exponential diophantine equation (n-1)(x) + (n+2)(y) = n(z) [PDF]

, 2020
Suppose that n is a positive integer. We show that the only positive integer solutions (n, x, y, z) of the exponential Diophantine equation (n - 1)(x) + (n + 2)(y) = nz, n >= 2, xyz not equal 0, are (3, 2, 1, 2), (3,1, 2, 3).
Yuan, Pingzhi, Bai, Hairong
core   +3 more sources

Two exponential diophantine equations [PDF]

Journal de théorie des nombres de Bordeaux, 2017
The equation 3 a + 5 b -
openaire   +1 more source

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

, 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

General Solution of the Diophantine equation involving Mersenne Prime [PDF]

, 2023
In this article, I study and solve the exponential Diophantine equation $M_p^{x} + (M_q + 1)^{y}= (lz)^2$ where $M_p$ and $M_q$ are Mersenne primes, $l$ is a prime number, and $x,y$, and $z$ are non-negative integers.
Ghosh, Arkabrata
core   +1 more source

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

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 Mathematics
Let 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, Florian Luca, Faith Shadow Zottor   +2 more
doaj   +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