1Department of Mathematics Aristotle University of Thessaloniki University Campus 541 24 Thessaloniki, Greece 2Department of Mathematics University of Ottawa 585 King Edward St. Ottawa, Ontario, Canada, K1N 6N5
Colloquium Mathematicum, Tome 105 (2006) no. 1, pp. 51-55
Let $p$ denote a prime number.
P. Samuel recently solved the problem of determining
all squares in the linear recurrence sequence $\{ T_n \}$,
where $T_n$ and $U_n$ satisfy $T_n^2-pU_n^2=1$. Samuel
left open the problem of determining all squares in
the sequence $\{ U_n \}$. This problem was recently
solved by the authors. In the present paper, we extend
our previous joint work by completely solving the equation
$U_n=bx^2$, where $b$ is a fixed positive squarefree integer.
This result also extends previous work of the second author.
Keywords:
denote prime number nbsp samuel recently solved problem determining squares linear recurrence sequence where satisfy pu samuel problem determining squares sequence nbsp problem recently solved authors present paper extend previous joint work completely solving equation where fixed positive squarefree integer result extends previous work second author
Affiliations des auteurs :
D. Poulakis
1
;
P. G. Walsh
2
1
Department of Mathematics Aristotle University of Thessaloniki University Campus 541 24 Thessaloniki, Greece
2
Department of Mathematics University of Ottawa 585 King Edward St. Ottawa, Ontario, Canada, K1N 6N5
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author = {D. Poulakis and P. G. Walsh},
title = {On the {Diophantine} equation $x^2-dy^4=1$
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journal = {Colloquium Mathematicum},
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D. Poulakis; P. G. Walsh. On the Diophantine equation $x^2-dy^4=1$
with prime discriminant II. Colloquium Mathematicum, Tome 105 (2006) no. 1, pp. 51-55. doi: 10.4064/cm105-1-6
