Scholz’s Third Conjecture: A Demonstration for Star Addition Chains ()
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.
DOI: 10.4236/am.2013.410A1001
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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 - 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.
Share and Cite:
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.
Conflicts of Interest
The authors declare no conflicts of interest.
References
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[1]
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A. Scholtz, “Aufgaben und Losungen, 253,” Jahresbericht der Deutsche Mathematiker-Vereinigung, Vol. 47, 1937, pp. 41-42.
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[2]
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A. Brauer, “On Addition Chains,” Bulletin of the American Mathematical Society, Vol. 45, No. 10, 1939, pp. 736-739.
http://dx.doi.org/10.1090/S0002-9904-1939-07068-7
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