On the exponential diophantine equation

Author: lgtc

August undefined, 2024

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 - … 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 …

Exponential Diophantine Equations Number theory

Web17 de abr. de 2009 · In this paper we give all positive integer solutions ( x, y, m, n) of the equation x2 + p2m = yn, gcd ( x, y) = 1, n > 2 satisfying 2 n of 2 ∤ n and p ≢ (−1) (p−1)/2 (mod 4 n. Type Research Article Information Bulletin of the Australian Mathematical Society , Volume 64 , Issue 1 , August 2001 , pp. 99 - 105 Web23 de jun. de 2024 · has only finitely many solutions $(x,y,z,m,n)$ satisfying $xyz\neq0$, $dax^{m}\neq bcy^{n}$ and $\min(m,n)\geq5$.. This theorem implies that equation has … truth knife

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

WebIn this paper, using an upper bound for solutions of ternary purely exponential Diophantine equations due to R. Scott and R. Styer, we prove that, for any positive integer n, if A >B3/8, then the equation (A2 n)x + (B2 n)y = ((A2 + B2)n)z has no positive integer solutions (x,y,z) with x > z > y; if B>A3/6, then it has no solutions ... WebThe Exponential Diophantine Equation . Yahui Yu 1 and Xiaoxue Li 2. Show more. Academic Editor: Abdelghani Bellouquid. Received 01 Apr 2014. Accepted 06 May 2014. … 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 … philips handel

On The Exponential Diophantine Equation (2^(2m+1) …

Web11 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 … 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 … philips handheld magnotech(Mihailescu’s Theorem/Catalan’s Conjecture) Let a, b, x, and y be positive integers satisfying the Diophantine equation $ a^x-b^y=1 $. Then the 4-tuple $(a,b,x,y)=(3,2,2,3)$is the unique solution of this equation. The next theorem is also significant to our work. Its proof can be seen in any undergraduate … Ver mais Recall Catalan’s conjecture, which dates back to 1844. It predicted that 8 and 9 were the only consecutive perfect powers among the positive … Ver mais The Diophantine equation where p is an odd prime, has a unique solution $(p,x,z)=(7,1,2)$ in $\mathbb {N}_0$. Ver mais (Fermat’s Last Theorem) Let a, b, c, and n be positive integers. Then, the equation $a^n + b^n = c^n$ admits no solution (a, b, c) if $n > 2$. By Fermat’s Last Theorem, we can … Ver mais Let p be an odd prime number, and x and zbe nonnegative integers. Case 1 ($x=0$): If $x=0$, then eDe (3) becomes $z^3=2,$ which implies that $z\not \in \mathbb {N}_0$. Hence, there is no nonnegative integer solution. Case … Ver mais truth knowledge belief

"Web1 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 … " - On the exponential diophantine equation

Exponential Diophantine Equations Number theory

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

On the exponential diophantine equation

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