On the diophantine equation x 2 + 2 a 3 b 73 c = y n

Murat Alan; Mustafa Aydin

Archivum Mathematicum (2023)

  • Volume: 059, Issue: 5, page 411-420
  • ISSN: 0044-8753

Abstract

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In this paper, we find all integer solutions ( x , y , n , a , b , c ) of the equation in the title for non-negative integers a , b and c under the condition that the integers x and y are relatively prime and n ≥ 3 . The proof depends on the famous primitive divisor theorem due to Bilu, Hanrot and Voutier and the computational techniques on some elliptic curves.

How to cite

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Alan, Murat, and Aydin, Mustafa. "On the diophantine equation $x^2+2^a3^b73^c=y^n $." Archivum Mathematicum 059.5 (2023): 411-420. <http://eudml.org/doc/299129>.

@article{Alan2023,
abstract = {In this paper, we find all integer solutions $ (x, y, n, a, b, c) $ of the equation in the title for non-negative integers $ a, b$ and $ c $ under the condition that the integers $ x $ and $ y $ are relatively prime and $ n \ge 3$. The proof depends on the famous primitive divisor theorem due to Bilu, Hanrot and Voutier and the computational techniques on some elliptic curves.},
author = {Alan, Murat, Aydin, Mustafa},
journal = {Archivum Mathematicum},
keywords = {diophantine equations; primitive divisor theorem; Ramanujan-Nagell equations},
language = {eng},
number = {5},
pages = {411-420},
publisher = {Department of Mathematics, Faculty of Science of Masaryk University, Brno},
title = {On the diophantine equation $x^2+2^a3^b73^c=y^n $},
url = {http://eudml.org/doc/299129},
volume = {059},
year = {2023},
}

TY - JOUR
AU - Alan, Murat
AU - Aydin, Mustafa
TI - On the diophantine equation $x^2+2^a3^b73^c=y^n $
JO - Archivum Mathematicum
PY - 2023
PB - Department of Mathematics, Faculty of Science of Masaryk University, Brno
VL - 059
IS - 5
SP - 411
EP - 420
AB - In this paper, we find all integer solutions $ (x, y, n, a, b, c) $ of the equation in the title for non-negative integers $ a, b$ and $ c $ under the condition that the integers $ x $ and $ y $ are relatively prime and $ n \ge 3$. The proof depends on the famous primitive divisor theorem due to Bilu, Hanrot and Voutier and the computational techniques on some elliptic curves.
LA - eng
KW - diophantine equations; primitive divisor theorem; Ramanujan-Nagell equations
UR - http://eudml.org/doc/299129
ER -

References

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