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| viXra.org > Number Theory > viXra:2211.0139 |
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Number Theory |
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Authors: Theophilus Agama
Applying the pothole method on the factors of numbers of the form $2^n-1$, we prove the inequality $$iota(2^n-1)leq frac{3}{2}n-left lfloor frac{n-2}{2^{lfloor frac{log n}{log 2}-1floor+1}}ight floor-lfloor frac{log n}{log 2}-1floor +frac{1}{4}(1-(-1)^n)+iota(n)$$ where $lfloor cdot floor$ denotes the floor function and $iota(n)$ the shortest addition chain producing $n$.
Comments: 6 Pages.
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[v1] 2022-11-23 17:50:54
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