Perfect Pell Powers

Author:

Cohn J. H. E.

Abstract

In the thirty years since it was proved that 0, 1 and 144 were the only perfect squares in the Fibonacci sequence [1, 9], several generalisations have been proved, but many problems remain. Thus it has been shown that 0, 1 and 8 are the only Fibonacci cubes [6] but there seems to be no method available to prove the conjecture that 0, 1, 8 and 144 are the only perfect powers.

Publisher

Cambridge University Press (CUP)

Subject

General Mathematics

Reference9 articles.

1. On Fibonacci and Lucas numbers which are perfect powers;London;Fibonacci Quart,1969

2. Five Diophantine Equations.

3. Squares in some recurrent sequences

4. Simplifying the solution of Ljunggren's equation X2+1=2Y4

5. Zur Theorie de Gleichung x2 + 1 = Dy4;Ljunggren;Avh. Norske Vid. Akad., Oslo,1942

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1. On perfect powers that are sums of cubes of a nine term arithmetic progression;Indagationes Mathematicae;2024-05

2. On the solutions of some Lebesgue–Ramanujan–Nagell type equations;International Journal of Number Theory;2024-04-06

3. On k-Fibonacci and k-Lucas numbers written as a product of two Pell numbers;Boletín de la Sociedad Matemática Mexicana;2024-02-17

4. On a class of Lebesgue-Ramanujan-Nagell equations;Periodica Mathematica Hungarica;2023-12-14

5. On Perfect Powers in $$k$$-Generalized Pell–Lucas Sequence;Mathematical Notes;2023-12

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