TITLE:
Scholz’s Third Conjecture: A Demonstration for Star Addition Chains
AUTHORS:
José Maclovio Sautto Vallejo, Agustín Santiago Moreno, Carlos N. Bouza Herrera, Verónica Campos Guzmán
KEYWORDS:
Addition Chain; Exponentiation; Short Chain; Scholz’s Conjecture
JOURNAL NAME:
Applied Mathematics,
Vol.4 No.10A,
September
30,
2013
ABSTRACT: This paper presents a brief demonstration of Scholz’s third conjecture [1] for n numbers such that their minimum chain addition is star type [2]. The demonstration is based on the proposal of an algorithm that takes as input the star-adding chain of a number n, and returns a string in addition to x = 2n - 1of length equal to l (n) + n - 1. As for any type addition chain star of a number n, this chain is minimal demonstrates the Scholz’s third Conjecture for such numbers.