Results 21 to 30 of about 1,510,077 (175)
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
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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
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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
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On the Exponential Diophantine Equation 3x - 2.5y = z2
, 2022 PP:27-30In this paper, we introduce the notion of the exponential Diophantine equation. We also did some characterisations of the Diophantine equation. In this article, we study and establish the theorem of the Diophantine equation 3x - 2.
Gope, Rathindra Chandra +1 more
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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
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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
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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
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四川大学学报. 自然科学版, 2022 Correlation functions play a key role in the statistical description of chaotic maps. The main concern of this paper is the calculation of correlation functions of the Tchebyscheff maps, which is traditionally handled by using the graph theoretical ...
ZHOU Xing-Wang
doaj
Small two-variable exponential Diophantine equations [PDF]
Mathematics of Computation, 1993 We examine exponential Diophantine equations of the form a b x = c d y + e a{b^x} = c{d^y} + e . Consider a ≤ 50 a \leq 50 , c ≤
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Communications on Pure and Applied Mathematics, Volume 79, Issue 9, Page 2107-2157, September 2026.ABSTRACT The leading‐order asymptotic behavior of the solution of the Cauchy initial‐value problem for the Benjamin–Ono equation in L2(R)$L^2(\mathbb {R})$ is obtained explicitly for generic rational initial data u0$u_0$. An explicit asymptotic wave profile uZD(t,x;ε)$u^\mathrm{ZD}(t,x;\epsilon)$ is given, in terms of the branches of the multivalued ...
Elliot Blackstone +3 more
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