Hostname: page-component-7dd5485656-zklqj Total loading time: 0 Render date: 2025-10-31T00:14:24.102Z Has data issue: false hasContentIssue false
  • English
  • Français

Perfect Pell Powers

Published online by Cambridge University Press:  18 May 2009

J. H. E. Cohn
J. H. E. Cohn
Affiliation:
Department of Mathematics, Royal Holloway University of London, Egham, Surrey TW20 0EX, England
Rights & Permissions [Opens in a new window]

Extract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

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.

Information

Type
Research Article
Information
Glasgow Mathematical Journal , Volume 38 , Issue 1 , January 1996 , pp. 19 - 20
Copyright
Copyright © Glasgow Mathematical Journal Trust 1996

References

REFERENCES

1.Cohn, J. H. E., On Square Fibonacci Numbers, J. London Math. Soc. 39 (1964) 537–540.CrossRefGoogle Scholar
2.Cohn, J. H. E., Eight Diophantine Equations, Proc. London Math. Soc. (3) 16 (1966) 153–166.CrossRefGoogle Scholar
3.Cohn, J. H. E., Five Diophantine Equations, Math. Scand. 21 (1967) 61–70.Google Scholar
4.Cohn, J. H. E., Squares in some recurrent sequences, Pacific J. Math. 41 (1972) 631–646.Google Scholar
5.Ljunggren, W., Zur Theorie de Gleichung x 2 + 1 = Dy 4, Avh. Norske Vid. Akad., Oslo 1, No. 5 (1942).Google Scholar
6.London, Hymie and Finkelstein, Raphael, On Fibonacci and Lucas numbers which are perfect powers, Fibonacci Quart. 5 (1969) 476–481.Google Scholar
7.Mordell, L. J., The diophantine equation y 2= Dx 4 + 1, J. London Math. Soc. 39 (1964) 161–164.Google Scholar
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.Wyler, O., Solution to Problem 5080, Amer. Math. Monthly 71 (1964) 220–222.Google Scholar