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Scholz’s Third Conjecture: A Demonstration for Star Addition Chains

DOI: 10.4236/am.2013.410A1001    2,863 Downloads   4,196 Views   Citations


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.

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The authors declare no conflicts of interest.

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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.


[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.

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