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**Jones, J.P., Diophantine representation of the Lucas numbers,
Fibonacci Quarterly 14 (1976), 134-134. MR 53:2818. **

The set of Lucas numbers *1,3,4,7,11,18,29,...* is defined by the
sequence *L _{n}* where

In this paper it is proved that the set of Lucas numbers is identical
with the set of positive values of a polynomial of the 9th degree in
two variables *x* and *y*,

as these two variables range over the positive integers:

*
*

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

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