The Fibonacci search — the substantiation, the number system and the hashing

Mathematical Modelling: Methods, algorithms, technologies

The article is aimed to prove the completeness of the Fibonacci search. The algorithm of the search allows representing the searched-for numbers as finite sequences (n-tuples) of a special type combined of the alphabet consisting of three symbols. The conversion of the tripartite record of a number into the admissible tuple results in the hashing procedure.