On the diophantine equation x 2 + 5 k 17 l = y n

István Pink; Zsolt Rábai

Communications in Mathematics (2011)

  • Volume: 19, Issue: 1, page 1-9
  • ISSN: 1804-1388

Abstract

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Consider the equation in the title in unknown integers ( x , y , k , l , n ) with x ≥ 1 , y > 1 , n ≥ 3 , k ≥ 0 , l ≥ 0 and gcd ( x , y ) = 1 . Under the above conditions we give all solutions of the title equation (see Theorem 1).

How to cite

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Pink, István, and Rábai, Zsolt. "On the diophantine equation $x^2+5^k17^l=y^n$." Communications in Mathematics 19.1 (2011): 1-9. <http://eudml.org/doc/196718>.

@article{Pink2011,
abstract = {Consider the equation in the title in unknown integers $(x,y,k,l,n)$ with $x \ge 1$, $y >1$, $n \ge 3$, $k \ge 0$, $l \ge 0$ and $\gcd (x,y)=1$. Under the above conditions we give all solutions of the title equation (see Theorem 1).},
author = {Pink, István, Rábai, Zsolt},
journal = {Communications in Mathematics},
keywords = {exponential diophantine equations; primitive divisors; exponential Diophantine equation; generalized Ramanujan-Nagell equation; primitive divisors; -integral points; MAGMA},
language = {eng},
number = {1},
pages = {1-9},
publisher = {University of Ostrava},
title = {On the diophantine equation $x^2+5^k17^l=y^n$},
url = {http://eudml.org/doc/196718},
volume = {19},
year = {2011},
}

TY - JOUR
AU - Pink, István
AU - Rábai, Zsolt
TI - On the diophantine equation $x^2+5^k17^l=y^n$
JO - Communications in Mathematics
PY - 2011
PB - University of Ostrava
VL - 19
IS - 1
SP - 1
EP - 9
AB - Consider the equation in the title in unknown integers $(x,y,k,l,n)$ with $x \ge 1$, $y >1$, $n \ge 3$, $k \ge 0$, $l \ge 0$ and $\gcd (x,y)=1$. Under the above conditions we give all solutions of the title equation (see Theorem 1).
LA - eng
KW - exponential diophantine equations; primitive divisors; exponential Diophantine equation; generalized Ramanujan-Nagell equation; primitive divisors; -integral points; MAGMA
UR - http://eudml.org/doc/196718
ER -

References

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