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Jones’ Characterization

J.P.Jones [1] proved  that the set of Fibonacci numbers is identical with the set of positive values of the following polynomial of the 5th degree in two variables x and y,  as these two variables range over the positive integers:

This means that each Fibonacci number is a value of the above polynomial, for some positive integers x and y, and vice verse,  each positive value of the polynomial is a Fibonacci number.  The result is not very practical since it is very hard to predict at which values of arguments the polynomial values are positive.

To compute sample values of Jones polynomial go to .

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