AM  Vol.4 No.10 A , October 2013
Scholz’s Third Conjecture: A Demonstration for Star Addition Chains
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.

Cite this paper
J. Vallejo, A. Moreno, C. Herrera and V. Guzmán, "Scholz’s Third Conjecture: A Demonstration for Star Addition Chains," Applied Mathematics, Vol. 4 No. 10, 2013, pp. 1-2. doi: 10.4236/am.2013.410A1001.
References
[1]   A. Scholtz, “Aufgaben und Losungen, 253,” Jahresbericht der Deutsche Mathematiker-Vereinigung, Vol. 47, 1937, pp. 41-42.

[2]   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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