SU\G(𝔸)/K·U

SOLUTIONS OF THE DIOPHANTINE EQUATION <i>x</i><sup><i>y</i></sup>+<i>y</i><sup><i>z</i></sup>+<i>z</i><sup><i>x</i></sup>=<i>n</i>!

Mihai Cipu, Florian Luca, Maurice Mignotte

Type: Article

Publication Date: 2008-04-21

Citations: 0

DOI: https://doi.org/10.1017/s0017089508004163

Abstract

Abstract We prove that the only solutions in coprime positive integers to the equation are ( x , y , z )=( n !–2, 1, 1, n ), n ≥3.

Locations

  • Glasgow Mathematical Journal - View - PDF

Similar Works

Action Title Year Authors
+ PDF Chat ON THE DIOPHANTINE EQUATION <i>x</i><sup>2</sup> + 5<sup><i>a</i></sup> 13<sup><i>b</i></sup> = <i>y</i><sup><i>n</i></sup> 2008 Fadwa S. Abu Muriefah
Florian Luca
Alain Togbé
+ PDF Chat The diophantine equation (<i>X</i>[<i>X</i> − 1])<sup>2</sup> = 3<i>Y</i>[<i>Y</i> − 1] 1976 Manoranjitham Veluppillai
+ On the Diophantine equation <i>x</i> <sup>2</sup> + <i>C</i>= <i>y<sup>n</sup> </i> for <i>C</i> = 2<sup> <i>a</i> </sup>3<sup> <i>b</i> </sup>17<sup> <i>c</i> </sup> and <i>C</i> = 2<sup> <i>a</i> </sup>13<sup> <i>b</i> </sup>17<sup> <i>c</i> </sup> 2016 Hemar Godinho
Diego Marques
Alain Togbé
+ PDF Chat On the equation \ x^y\pm y^x=\prod n_i! 2000 Florian Luca
Maurice Mignotte
Y. Arun Roy
+ PDF Chat On the Diophantine equation x<sup>2</sup>+ 2<sup>α</sup>13<sup>β</sup>= y<sup>n</sup> 2009 Florian Luca
Alain Togbé
+ ON THE DIOPHANTINE EQUATION x<sup>2</sup> + 2<sup>a</sup> · 5<sup>b</sup> = y<sup>n</sup> 2008 Florian Luca
Alain Togbé
+ PDF Chat On the Diophantine Equation <i>a</i> <i> <sup>x</sup> </i> +(<i>a</i> +2)<i> <sup>y</sup> </i> = <i>z</i> <sup>2</sup> Where <i>a</i> ≡ 5 (mod 42) 2020 Rakporn Dokchann
Apisit Pakapongpun
+ A note on the diophantine equation (<i>x</i><sup><i>m</i></sup> − l) / (<i>x</i> − 1) = <i>y</i><i><sup>n</sup></i> + l 1994 LE Mao-hua
+ PDF Chat ON THE NUMBER OF SOLUTIONS OF THE DIOPHANTINE EQUATION<i>ax</i><sup><i>m</i></sup>−<i>by</i><sup><i>n</i></sup>=<i>c</i> 2010 Bo He
Alain Togbé
+ PDF Chat A note on the ternary Diophantine equation <i>x</i> <sup>2</sup> − <i>y</i> <sup>2</sup> <i> <sup>m</sup> </i> = z<i> <sup>n</sup> </i> 2021 Attila Bérczes
LE Mao-hua
István Pink
Gökhan Soydan
+ Solutions of the Diophantine Equations p x + (p + 1)y + (p + 2)z = M 2 for Primes p ≥ 2 when 1 ≤ x, y, z ≤ 2 2020 Nechemia Burshtein
+ PDF Chat On The Diophantine Equation <i>x<sup>a</sup></i> + <i>y<sup>a</sup> </i>= <i>p<sup>k</sup>z<sup>b</sup></i> 2017 Keng Yarn Wong
Hailiza Kamarulhaili
+ PDF Chat On the Diophantine equation (x<sup>m</sup>-1)/(x-1) = (y<sup>n</sup>-1)/(y-1) 2002 Yann Bugeaud
T. N. Shorey
+ PDF Chat On the exponential Diophantine equation <i>m<sup>x</sup> </i>+(<i>m</i>+1)<i> <sup>y</sup> </i>=(1+<i>m</i>+<i>m</i> <sup>2</sup>)<i> <sup>z</sup> </i> 2021 Murat Alan
+ PDF Chat On the equation <i>x</i><sup>2</sup> + 2<sup><i>a</i></sup> · 3<sup><i>b</i></sup> = <i>y</i><sup><i>n</i></sup> 2002 Florian Luca
+ NATURE OF THE DIOPHANTINE EQUATION 4X + 12Y = Z2 2021 S.P. Behera
A.C. Panda
+ PDF Chat ON THE DIOPHANTINE EQUATION (8<i>n</i>)<sup><i>x</i></sup>+(15<i>n</i>)<sup><i>y</i></sup>=(17<i>n</i>)<sup><i>z</i></sup> 2012 Zhi-Juan Yang
Min Tang
+ PDF Chat THE EXPONENTIAL DIOPHANTINE EQUATION <i>n<sup>x</sup></i> + (<i>n</i> + 1)<sup><i>y</i></sup> = (<i>n</i> + 2)<sup><i>z</i></sup> REVISITED 2009 Bo He
Alain Togbé
+ On the Diophantine equation (x m −1)/(x−1) = (y n −1)/(y−1) 2002 Yann Bugeaud
T. N. Shorey
+ Solution of the Diophantine Equation $ x_{1}x_{2}x_{3}\cdots x_{m-1}=z^n $ 2014 Zahid Raza
Hafsa Masood Malik

Works That Cite This (0)

Action Title Year Authors

Works Cited by This (3)

Action Title Year Authors
+ Linear forms in p-adic logarithms and the Diophantine equation formula here 1999 Yann Bugeaud
+ Minoration effective de la distancep-adique entre puissances de nombres algébriques 1996 Yann Bugeaud
Laurent Michel
+ PDF Chat On the equation \ x^y\pm y^x=\prod n_i! 2000 Florian Luca
Maurice Mignotte
Y. Arun Roy