Name
Title | ||
|---|---|---|
Some Properties of Nonstar Steps in Addition Chains and New Cases Where the Scholz Conjecture Is True |
Abstract | ||
|---|---|---|
Let ℓ(n) be the smallest possible length of addition chains for a positive integer n. Then Scholz conjectured that ℓ(2n−1)≤n+ℓ(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. |
Year | DOI | Venue |
|---|---|---|
2002 | 10.1006/jagm.2002.1212 | Journal of Algorithms |
Keywords | Field | DocType |
addition chains,Hansen chains,nonstar steps,Scholz's conjecture | Integer,Discrete mathematics,Combinatorics,Scholz conjecture,Mathematics,Binary number,Addition chain | Journal |
Volume | Issue | ISSN |
42 | 2 | 0196-6774 |
Citations | PageRank | References |
6 | 0.59 | 1 |
Authors | ||
2 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Hatem M. Bahig | 1 | 23 | 7.53 |
| Ken Nakamula | 2 | 17 | 3.68 |