Goormaghtigh equation

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August undefined, 2024

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 …

On the Diophantine Equation of (x^m-1)/(x-1)=(y^n-1)/(y-1)

Web1. Introduction. An equation of Goormaghtigh [4] is as follows: (1) x x m− − 1 1 = yn − 1 y − 1 in integers x > 1,y > 1,m > 2,n > 2 with x 6= y. This equation asks for integers with all the digits equal to one with respect to two distinct bases. It has been conjectured that equation (1) has only ﬁnitely many solutions. Goormaghtigh [4 ... WebMay 26, 2024 · An Equation of Goormaghtigh and Diophantine Approximations T. Shorey Mathematics, Computer Science 2002 TLDR An extension of (1) with m = 3 is … chemistry past papers topical

A note on the Goormaghtigh equation SpringerLink

WebGoormaghtigh equation Asked 10 years, 1 month ago Modified 10 years, 1 month ago Viewed 288 times 5 For fixed prime p and q is it true that the following equation has at … WebOn Goormaghtigh’s equation x 3 -1 x-1=y n -1 y-1 Article Jan 2002 Maohua Le View Linear forms in two logarithms and interpolation determinants Article Jan 1994 Michel … 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 $N$ … flightgear software

An Abundancy Result for the Two Prime Power Case ... - HIKARI Ltd

The equation $x^4+2^ny^4=z^4$ in algebraic number fields

WebIn the second part of this thesis, we show that, by fixing one exponent, there exists an effectively computable constant bounding the solutions of a Goormaghtigh equation under certain conditions. For small values of this fixed exponent, we … WebLet x, y, z, n, α ∈ ℤ with α ≥ 1, p and n ≥ 5 primes. In 2011, Michael Bennett, Florian Luca and Jamie Mulholland showed that the equation involving a twisted sum of cubes [equation omitted] has no pairwise coprime nonzero integer solutions p ≥ 5,n ≥ p²p and p ∉ S where S is the set of primes q for which there exists an elliptic curve of conductor NE ∈ … chemistry past papers o level topicalWeb(with S. Yang, B. He), Diophantine equations with products of consecutive values of a quadratic polynomial. ... , On the number of solutions of Goormaghtigh equation for given x and y. Indag. Mathem., N.S., 19 (1) (2008), 65-72. On the solutions of a parametric family of cubic Thue equations. chemistry past question waec

"Web1276. On a cubic diophantine equation - Volume 21 Issue 247 " - Goormaghtigh equation

Goormaghtigh equation

WebGOORMAGHTIGH’S EQUATION : SMALL PARAMETERS MICHAEL A. BENNETT, BEN GARBUZ AND ADAM MARTENS 1. Introduction The frequently studied polynomial … WebMar 3, 2024 · In this paper, as a parallel problem of [11] for each integer k ≥2, we consider the set E (X) of positive integers b ≤ X which satisfy the condition of congruent solubility and that the equation. a_1 p_1^2 + a_2 p_2^2 + a_3 p_3^k = b. is insoluble in primes p j. We obtain Card E (X)≤X 1-ε. Our result extends the wellknown classical ...

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WebThe following individuals certify that they have read, and recommend to the Fac-ulty of Graduate and Postdoctoral Studies for acceptance, the thesis entitled: Computing elliptic c WebYu. V. Nesterenko and T.N. Shorey, On an equation of Goormaghtigh, Acta Arith. 83 (1998), 381–389. MathSciNet MATH Google Scholar K. Ratat, L’Intermédiaire des Mathématiciens 23 (1916), 150. Google Scholar

WebThe Goormaghtigh conjecture may be expressed as saying that 31 (111 in base 5, 11111 in base 2) and 8191 (111 in base 90, 1111111111111 in base 2) are the only two … In mathematics, the Goormaghtigh conjecture is a conjecture in number theory named for the Belgian mathematician René Goormaghtigh. The conjecture is that the only non-trivial integer solutions of the exponential Diophantine equation satisfying and are and

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 ... Webtitle = "AN OLD and NEW APPROACH to GOORMAGHTIGH'S EQUATION", abstract = "We show that if n ≥ 3 is a fixed integer, then there exists an effectively computable constant …

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 ...

WebOct 22, 2024 · We show that if c is a positive integer satisfying $$2c-1=3p^l\ \hbox{or}\ 2c-1=5p^l$$ with p prime and l positive integer, then the equation $${x^2 + (2c-1)^m}=c^n$$ has only the positive integer solution $$(x,m,n)=(c-1,1,2)$$ without any congruence condition on a prime p. flight gear simulator 2020WebIt can be shown from Maxwell’s equations that superimposition of incoming and reflected waves yields a standing wave within the IRE, established normal to the totally reflecting surface, and an electromagnetic disturbance exists in the rarer medium beyond the reflecting interface. ... Goormaghtigh E, Ruysschaert JM, Raussens V. Evaluation of ... chemistry past papers igcse grade 9WebOn an equation of Goormaghtigh by. Authors. Publication date 2015. Publisher. Abstract (1) xm − 1 x − 1 = yn − . text; Similar works. Full text. CiteSeerX Provided a free PDF … flight gear simulator vs fsxWebAn Abundancy Result for the Two Prime Power Case ... - HIKARI Ltd flight gear simulator rocket codeWebIn mathematics, the Goormaghtigh conjecture is a conjecture in number theory named for the Belgian mathematician René Goormaghtigh. The conjecture is that the only non … chemistry past papers n5WebOn an equation of Goormaghtigh by Yu. V. Nesterenko (Moscow) and T. N. Shorey (Mumbai) Dedicated to Professor A. Schinzel on his 60th birthday 1. Introduction. An … flightgear source codeWebOct 16, 2024 · (1.1) has only two solutions (x,\ y,\ m,\ n)= (2,\ 5,\ 5,\ 3) and (2,\ 90,\ 13,\ 3). ( 1.1) is usually called the Goormaghtigh equation. This is a very difficult problem in number theory. It was solved for some special cases (see [ 1, 2, 3, 4, 7, 8, 9, 11, 16, 18] and the … chemistry patent attorney