On the Diophantine equation x² - dy⁴ = 1 with prime discriminant II

D. Poulakis, and P. G. Walsh. "On the Diophantine equation x² - dy⁴ = 1 with prime discriminant II." Colloquium Mathematicae 105.1 (2006): 51-55. <http://eudml.org/doc/286471>.

@article{D2006,
abstract = {Let p denote a prime number. P. Samuel recently solved the problem of determining all squares in the linear recurrence sequence \{Tₙ\}, where Tₙ and Uₙ satisfy Tₙ² - pUₙ² = 1. Samuel left open the problem of determining all squares in the sequence \{Uₙ\}. This problem was recently solved by the authors. In the present paper, we extend our previous joint work by completely solving the equation Uₙ = bx², where b is a fixed positive squarefree integer. This result also extends previous work of the second author.},
author = {D. Poulakis, P. G. Walsh},
journal = {Colloquium Mathematicae},
keywords = {Pell equation; linear recurrence sequence; quartic Diophantine equation},
language = {eng},
number = {1},
pages = {51-55},
title = {On the Diophantine equation x² - dy⁴ = 1 with prime discriminant II},
url = {http://eudml.org/doc/286471},
volume = {105},
year = {2006},
}

TY - JOUR
AU - D. Poulakis
AU - P. G. Walsh
TI - On the Diophantine equation x² - dy⁴ = 1 with prime discriminant II
JO - Colloquium Mathematicae
PY - 2006
VL - 105
IS - 1
SP - 51
EP - 55
AB - Let p denote a prime number. P. Samuel recently solved the problem of determining all squares in the linear recurrence sequence {Tₙ}, where Tₙ and Uₙ satisfy Tₙ² - pUₙ² = 1. Samuel left open the problem of determining all squares in the sequence {Uₙ}. This problem was recently solved by the authors. In the present paper, we extend our previous joint work by completely solving the equation Uₙ = bx², where b is a fixed positive squarefree integer. This result also extends previous work of the second author.
LA - eng
KW - Pell equation; linear recurrence sequence; quartic Diophantine equation
UR - http://eudml.org/doc/286471
ER -