Edouard Zeckendorf shewed that every positive integer can be represented uniquely as a sum of distinct non-consecutive Fibonacci numbers, with $ F_2 $ (but not $ F_1 $) being used for 1. Arithmetic on integers represented in Zeckendorf form is more complicated than for integers represented in binary form. But, integer multiplication can readily be performed by adapting the Russian Peasant method, and integer division can readily be performed by adapting an Ancient Egyptian method. |
Keywords
Zeckendorf, arithmetic algorithms, Russian Peasant multiplication, Ancient Egyptian division
Math Review Classification
Primary 11B39
; Secondary 03H15
Last Updated
2002-3-21
Length
9 pages
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