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

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Poulakis D., Walsh P.

Colloquium Mathematicum

2006

tom 105

nr 1

51-55

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.

Ograniczanie wyników

1 Colloquium Mathematicum

1 Poulakis D.

1 Walsh P.

1 2006

Wyniki wyszukiwania

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