Number Theory

    

On a Certain Inequality on Addition Chains

Authors: Theophilus Agama

In this paper we prove that there exists an addition chain producing 2^n-1 of length delta(2^n-1) satisfying the inequality delta(2^n-1)leq 2n-1-2left lfloor frac{n-1}{2^{lfloor frac{log n}{log 2}floor}}ight floor+lfloor frac{log n}{log 2}flooronumber where lfloor cdot floor denotes the floor function.

Comments: 5 Pages. This paper improves on the bounds in previous works and it is more explicit.

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Submission history

[v1] 2022-07-19 01:43:32

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