On the exponential diophantine equation

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Web4 de dez. de 2024 · In this paper we show that the Diophantine equations 17x +83y = z2 and 29x +71y = z2 has a unique non – negative integer solution (x,y,z) = (1,1,10) Keywords—Exponential Diophantine equation , integer solutions 1. Introduction In the past, researchers have been interested in studying various forms of Diophantine … Web24 de out. de 2024 · We show that the exponential Diophantine equation $$ (m^2+m+1)^x+m^y=(m+1)^z $$ has no positive integer solutions ot. Skip to main …

Diophantine Equation -- from Wolfram MathWorld

WebIn mathematics, a Diophantine equation is an equation, typically a polynomial equation in two or more unknowns with integer coefficients, such that the only solutions of interest are the integer ones. A linear Diophantine equation equates to a constant the sum of two or more monomials, each of degree one. An exponential Diophantine equation is one in … Webor not a given exponential diophantine equation is solvable. Suppose all exponential diophantine equations are numbered effectively according to some definite scheme, and let Cd be the ith equation in this ordering. Also let x be some fixed variable and let Cj(u) be the equation obtained from St by substituting u for x throughout Cd. We can easily cibc income plus performance morningstar

1 Exponential Diophantine equations - CMU

Webrelevant for the exponential Diophantine equations I want to discuss, I refer for such results to [Ba77] for developments until 1977 and to [FeNe98,Wa00] for later developments. Many more results and references can be found there, also for the rational case. Relevant for the theory of exponential Diophantine equations are the results on linear ... Web1 Exponential Diophantine equations Diophantine equations are just equations we solve with the constraint that all variables must be integers. These are generally really hard to solve (for example, the famous Fermat’s Last Theorem is an example of a Diophantine equation). Today, we will begin by focusing on a special kind of Diophantine ... WebThe authors present, in a clear and unified fashion, applications to exponential diophantine equations and linear recurrence sequences of the Gelfond-Baker theory of linear forms … dgft complaint status

$arXiv:2001.09617v1 [math.NT] 27 Jan 2024$

On the exponential diophantine equation

An exponential diophantine equation Bulletin of the Australian ...

Web15 de jan. de 2024 · In 2002, F. Luca and G. Walsh solved the Diophantine equation in the title for all pairs (a,b) such that 1 Web20 de mai. de 2024 · On the Diophantine equation 1 k + 2 k + · · · + xk = yn M. Bennett, K. Gyory, Á. Pintér Mathematics 2004 In this paper, we resolve a conjecture of Schäffer on the solvability of Diophantine equations of the shape 1k + 2k + · · · + xk = yn, for 1 k 11. Our method, which may, with a modicum of effort, be… Expand 27 PDF

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Web1 de mai. de 2024 · Solving Exponential Diophantine Equations. Find all positive integers a, b, c > 1, all relatively prime with respect to each other such that b ∣ 2 a + 1, c ∣ 2 b + 1, a ∣ 2 c + 1. It is easy to see that all of a, b, c are odd. Suppose 3 ∣ a then we have 3 ∣ 2 c + 1 and as ( a, c) = 1 so we have c = 6 k + 1 or c = 6 k + 5 for some k. WebSo in this video I have solved another diophantine equation which involves modular argument and the idea is to divide it into two cases.Interestingly it has ...

Web28 de mar. de 2024 · Finding the solution of Diophantine equations have many challenges for scholars due to absence of generalize methods. In the present paper, author studied … Web1 de set. de 2009 · THE EXPONENTIAL DIOPHANTINE EQUATION nx + (n + 1)y = (n + 2)z REVISITED - Volume 51 Issue 3. To save this article to your Kindle, first ensure [email protected] is added to your Approved Personal Document E-mail List under your Personal Document Settings on the Manage Your Content and Devices page …

Web10 de ago. de 2024 · Observe that, for x=1, the Diophantine equation ( 1.4) becomes F_n = F_ {n+1} - F_ {n-1} =F_m , which gives m=n, and for x=2, F_ {2n} = F_ {n+1}^2 - F_ {n-1}^2=F_m, gives m=2n. When n=1, we have that F_ {2}^x - … Web1 de nov. de 2024 · On exponential Diophantine equation 17 x +83 y = z 2 and 29 x +71 y = z 2. Komon Paisal 1 and Pailin Chayapham 1. Published under licence by IOP Publishing Ltd Journal of Physics: Conference Series, Volume 2070, Second International Conference on Advances in Physical Sciences and Materials 2024(ICAPSM 2024) 12-13 August …

WebThe authors present, in a clear and unified fashion, applications to exponential diophantine equations and linear recurrence sequences of the Gelfond-Baker theory of linear forms in logarithms of algebraic numbers. Topics covered include the Thue equations, the generalised hyperelliptic equation, and the Fermat and Catalan equations.

Web9 de abr. de 2014 · In this paper, using some properties of exponential diophantine equations and some results on the existence of primitive divisors of Lucas numbers, we … dgft complaint registrationWebSome results concerning the exponential Diophantine equation ... In this paper, we examine, under some assumptions on the residue of a modulo an odd prime factor p of … cibc hr addressWebIn mathematics, a Diophantine equation is an equation, typically a polynomial equation in two or more unknowns with integer coefficients, such that the only solutions of interest … cibc infinite aeroplan visaWeb11 de jul. de 2024 · ON THE EXPONENTIAL DIOPHANTINE EQUATION (a n − 1)(b n − 1) = x 2. July 2024; Bulletin of the Belgian Mathematical Society, Simon Stevin 27(2):161 … dgft complaintWeb1 Exponential Diophantine equations Diophantine equations are just equations we solve with the constraint that all variables must be integers. These are generally really … cibc in cornwall ontarioWeb1 de set. de 2015 · In this text, the exclusive exponential Diophantine equation px + (p + 1)y= z2such that the sum of integer powers and of two consecutive prime numbers … dgft common portalWebSuch equations are called Diophantine equations, those Diophantine equations with variable exponents are called polynomial-exponential equations. Let Z, N, Qdenote the … cibc ingersoll ontario