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**Jones, J.P., Diophantine representation of the Fibonacci numbers,
Fibonacci Quarterly 13 (1975), 84-88. MR 52:3035. **

The set of Fibonacci numbers *0,1,1,2,3,5,8,13,21,34,55,...* is
defined by the sequence *F _{0} = 0, F_{1} = 1 and
F_{n+2} = F_{n+1} + F_{n}*.

In this paper it is proved that the set of Fibonacci numbers is identical
with the set of positive values of a polynomial of the 5th degree in two
variables *x* and *y*,

as these two variables range over the positive integers:

*
*

Each Fibonacci number is a value of the above polynomial, for some
positive integers *x* and *y*. Also each positive value of
the polynomial is a Fibonacci number.

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