Selected topics in addition chains

dc.creatorGiese, Robert Paul
dc.description.abstractW. R. Utz conjectured that [lowercase l](2n) = [lowercase l](n) + 1. D. Knuth found four counterexamples to Utz's conjecture. He then modified it to [lowercase l](2n) > [lowercase l](n) and more generally [lowercase l](mn) > [lowercase l](n). This dissertation contains an infinite number of counterexamples to Knuth's modification of the Utz conjecture. A conjecture is proposed by this author that has the theorems of Utz, Subbarao, and Knuth concerning addition chains as corollaries: If [lowercase l](n) = [lambda](n) + k, then [nu](n) < 2[raised k]. Knuth introduced a sequence c, exhibited the first few terms of the sequence, and proposed an asymptotic limit theorem. In this paper an asymptotic limit theorem is proven for c: If lim (c(r))/([Phi][raised r]) = 1, then [Phi] = 2.
dc.description.departmentMathematics, Department of
dc.format.digitalOriginreformatted digital
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dc.titleSelected topics in addition chains
dcterms.accessRightsThe full text of this item is not available at this time because it contains documents that are presumed to be under copyright and are accessible only to users who have an active CougarNet ID. This item will continue to be made available through interlibrary loan. of Natural Sciences and Mathematics, Department of of Houston of Philosophy


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