Perfect Pell Powers
Glasgow mathematical journal, Tome 38 (1996) no. 1, pp. 19-20

Voir la notice de l'article provenant de la source Cambridge University Press

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.
Cohn, J. H. E. Perfect Pell Powers. Glasgow mathematical journal, Tome 38 (1996) no. 1, pp. 19-20. doi: 10.1017/S0017089500031207
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[1] 1.Cohn, J. H. E., On Square Fibonacci Numbers, J. London Math. Soc. 39 (1964) 537–540. Google Scholar | DOI

[2] 2.Cohn, J. H. E., Eight Diophantine Equations, Proc. London Math. Soc. (3) 16 (1966) 153–166. Google Scholar | DOI

[3] 3.Cohn, J. H. E., Five Diophantine Equations, Math. Scand. 21 (1967) 61–70. Google Scholar

[4] 4.Cohn, J. H. E., Squares in some recurrent sequences, Pacific J. Math. 41 (1972) 631–646. Google Scholar

[5] 5.Ljunggren, W., Zur Theorie de Gleichung x + 1 = Dy 4, Avh. Norske Vid. Akad., Oslo 1, No. 5 (1942). Google Scholar

[6] 6.London, Hymie and Finkelstein, Raphael, On Fibonacci and Lucas numbers which are perfect powers, Fibonacci Quart. 5 (1969) 476–481. Google Scholar

[7] 7.Mordell, L. J., The diophantine equation y 2= Dx 4 + 1, J. London Math. Soc. 39 (1964) 161–164. Google Scholar

[8] 8.Steiner, Ray and Tzanakis, Nikos, Simplifying the solution of Ljunggren's equation X 2 + 1 = 2Y 4, J. Number Theory, 37 (1991) 123–132. Google Scholar

[9] 9.Wyler, O., Solution to Problem 5080, Amer. Math. Monthly 71 (1964) 220–222. Google Scholar

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