Representations found by the greedy algorithm

[Alec Mihailovs]

From: "Max A." <maxale at gmail.com>

> Theorem 2. For any non-negative integer N, there exists an unique 
> representation
> N = c1*F(1) - c2*F(2) + c3*F(3) - ...
> where every coefficient is either 0 or 1 with no adjacent unit 
> coefficients.

That is true also for negative integers and 0. I remember seeing it 
somewhere called ternary Fibonacci number system, with a suggestion of using 
it in computers instead of binary system. I couldn't find a reference 
though. As far as I recall, in some Russian articles it was also called the 
Mendeleev number system (following the idea that everything was invented in 
Russia :) Again, I couldn't find a reference.

Alec