| viXra.org > Number Theory > viXra:2205.0028 |
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| viXra.org > Number Theory > viXra:2205.0028 |
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Number Theory |
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Authors: Theophilus Agama
In this paper we extend the so-called notion of addition chains and prove an analogue of Scholz's conjecture on this chain. In particular, we obtain the inequality $$\iota^{\lfloor \frac{n-1}{2}\rfloor}(2^n-1)\leq n+\iota(n)$$ where $\iota(n)$ and $\iota^{\lfloor \frac{n-1}{2}\rfloor}(n)$ denotes the length of the shortest addition chain and the shortest addition chain of degree $\lfloor \frac{n-1}{2}\rfloor$, respectively, producing $n$.
Comments: 4 Pages.
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[v1] 2022-05-05 11:51:55
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