Glasgow Mathematical Journal

Research Article

Perfect Pell Powers

J. H. E. Cohna1

a1 Department of Mathematics, Royal Holloway University of London, Egham, Surrey TW20 0EX, England

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.

(Received May 09 1994)