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

DOI: 10.4236/am.2013.410A1001    2,776 Downloads   4,069 Views   Citations

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.

Conflicts of Interest

The authors declare no conflicts of interest.

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. 10A, 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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