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Some Properties of Nonstar Steps in Addition Chains and New Cases Where the Scholz Conjecture Is True

✍ Scribed by Hatem M. Bahig; Ken Nakamula

Publisher: Elsevier Science
Year: 2002
Tongue: English
Weight: 114 KB
Volume: 42
Category: Article
ISSN: 0196-6774
DOI: 10.1006/jagm.2002.1212

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✦ Synopsis

Let n be the smallest possible length of addition chains for a positive integer n. Then Scholz conjectured that 2 n -1 ≤ n + n -1, which still remains open. It is known that the Scholz conjecture is true when ν n ≤ 4, where ν n is the number of 1's in the binary representation of n. In this paper, we give some properties of nonstar steps in addition chains and prove that the Scholz conjecture is true for infinitely many new integers including the case where ν n = 5.  2002 Elsevier Science (USA)