On the Diophantine equation x 2 + 2 α 5 β 17 γ = y n

Hemar Godinho; Diego Marques; Alain Togbé

Communications in Mathematics (2012)

  • Volume: 20, Issue: 2, page 81-88
  • ISSN: 1804-1388

Abstract

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In this paper, we find all solutions of the Diophantine equation x 2 + 2 α 5 β 17 γ = y n in positive integers x , y ≥ 1 , α , β , γ , n ≥ 3 with gcd ( x , y ) = 1 .

How to cite

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Godinho, Hemar, Marques, Diego, and Togbé, Alain. "On the Diophantine equation $x^2+2^\alpha 5^\beta 17^\gamma =y^n$." Communications in Mathematics 20.2 (2012): 81-88. <http://eudml.org/doc/251384>.

@article{Godinho2012,
abstract = {In this paper, we find all solutions of the Diophantine equation $x^2+2^\alpha 5^\beta 17^\gamma = y^n$ in positive integers $x,y\ge 1$, $\alpha ,\beta ,\gamma ,n\ge 3$ with $\gcd (x,y)=1$.},
author = {Godinho, Hemar, Marques, Diego, Togbé, Alain},
journal = {Communications in Mathematics},
keywords = {Diophantine equation; exponential equation; primitive divisor theorem; exponential Diophantine equation},
language = {eng},
number = {2},
pages = {81-88},
publisher = {University of Ostrava},
title = {On the Diophantine equation $x^2+2^\alpha 5^\beta 17^\gamma =y^n$},
url = {http://eudml.org/doc/251384},
volume = {20},
year = {2012},
}

TY - JOUR
AU - Godinho, Hemar
AU - Marques, Diego
AU - Togbé, Alain
TI - On the Diophantine equation $x^2+2^\alpha 5^\beta 17^\gamma =y^n$
JO - Communications in Mathematics
PY - 2012
PB - University of Ostrava
VL - 20
IS - 2
SP - 81
EP - 88
AB - In this paper, we find all solutions of the Diophantine equation $x^2+2^\alpha 5^\beta 17^\gamma = y^n$ in positive integers $x,y\ge 1$, $\alpha ,\beta ,\gamma ,n\ge 3$ with $\gcd (x,y)=1$.
LA - eng
KW - Diophantine equation; exponential equation; primitive divisor theorem; exponential Diophantine equation
UR - http://eudml.org/doc/251384
ER -

References

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