Hatem M. Bahig

Notes on Number Theory and Discrete Mathematics

Print ISSN 1310–5132, Online ISSN 2367–8275

Volume 28, 2022, Number 2, Pages 276–280

DOI: 10.7546/nntdm.2022.28.2.276-280

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## Details

### Authors and affiliations

**Hatem M. Bahig**

*Department of Mathematics, Faculty of Science, Ain Shams University
Cairo, Egypt*

### Abstract

Given a positive integer , an addition chain for is an increasing sequence of positive integers such that for each for some . In 1937, Scholz conjectured that *for each positive integer* , where denotes the minimal length of an addition chain for In 1993, Aiello and Subbarao stated the apparently stronger conjecture that *there is an addition chain for* *with length equals to* We note that the Aiello–Subbarao conjecture is not stronger than the Scholz (also called the Scholz–Brauer) conjecture.

### Keywords

- Addition chain
- Aiello–Subbarao’s conjecture
- Scholz–Brauer’s conjecture

### 2020 Mathematics Subject Classification

- 11Y16
- 11Y55

### References

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### Manuscript history

- Received: 21 January 2021
- Revised: 14 April 2022
- Accepted: 9 May 2022
- Online First: 10 May 2022

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## Cite this paper

Bahig, H. M. (2022). A note on the Aiello–Subbarao conjecture on addition chains. *Notes on Number Theory and Discrete Mathematics*, 28(2), 276-280, DOI: 10.7546/nntdm.2022.28.2.276-280.