Author(s)

José Maclovio Sautto Vallejo, Agustín Santiago Moreno, Carlos N. Bouza Herrera, Verónica Campos Guzmán

Facultad de Matemática y Computación, Universidad de la Habana, Ciudad de La Habana, Cuba.
Facultad de Matemáticas, Universidad Autónoma de Guerrero, Guerrero, México.
Universidad Autónoma de Guerrero, Unidad Académica de Ciencias y Tecnologías de la Información, Guerrero, México.

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 - 1  of 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.

Addition Chain; Exponentiation; Short Chain; Scholz’s Conjecture

J. Vallejo, A. Moreno, C. Herrera and V. Guzmán, "Scholz’s Third Conjecture: A Demonstration for Star Addition Chains," Applied Mathematics, Vol. 4 No. 10A, 2013, pp. 1-2. doi: 10.4236/am.2013.410A1001.