WebOct 16, 2024 · Request PDF A note on the Goormaghtigh equation Let p be an odd prime. By using a lower bound for linear forms in logarithms of two algebraic numbers, we prove that if \(p>10^{24}\), 2 is a ... WebJun 21, 2006 · In this paper, we show that this equation (2) has no exceptional solution when n = 4. We consider special Diophantine equations with integral coefficient and seek integral or rational solutions.

On the diophantine equation - Mathematics Stack Exchange

WebOct 5, 2024 · I have a question regarding Goormaghtigh conjecture on the Diophantine equation $$\frac {x^m-1} {x-1}=\frac {y^n-1} {y-1}.$$ Suppose that a positive integer $N$ … Web[16], [28]), and Goormaghtigh's equation (e.g. [3]). The most striking of such applications is the reduction, due to Bennett and Dahmen [2], of asymptotic cubic superelliptic equations to cubic ... thzy humidifier

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WebJun 1, 2011 · This equation has been considered by many authors from variety of standpoints; several subsets of the set {a,b, r, s, x, y} have been treated as the unknowns. ere we will consider only the case in which a, b, r, s, and c are given. ... On the number of solutions of Goormaghtigh equation for given x and y. Indag. Math. (N.S.), 19 (1) … WebMar 1, 2008 · In fact, we show that the Goormaghtigh equation x m − 1 x − 1 = y n − 1 y − 1, x > 1, y > 1, m > 1, n > 1, x < y, for x, y, m, n ∈ ℕ.has at most 1 solution (m, n) for … WebOn the number of solutions of Goormaghtigh equation for given x and y @article{He2008OnTN, title={On the number of solutions of Goormaghtigh equation for given x and y}, author={Bo He and Alain Togb{\'e}}, journal={Indagationes Mathematicae}, year={2008}, volume={19}, pages={65-72} } B. He, A. Togbé; Published 1 March 2008; … the law of mass