WebAn exponential Diophantine equation is one for which exponents of the terms of the equation can be unknowns. Diophantine problems have fewer equations than … Web26 de mar. de 2014 · ON THE EXPONENTIAL DIOPHANTINE EQUATION - Volume 90 Issue 1. 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 of your Amazon account.
On the Exponential Diophantine Equation
(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 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 ... five letter words ends in al
Equation - Wikipedia
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 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 … Web31 de mar. de 2024 · We examine exponential Diophantine equations of the form a{b^x} = c{d^y} + e . Consider a ≤ 50 , c ≤ 50 , \vert e\vert ≤ 1000 , and b and d from the set of … can i rent a truck with a fifth wheel hitch