A note on closed addition chains and complete numbers

Theophilus Agama

Paper 2025/833

A note on closed addition chains and complete numbers

Theophilus Agama

, Université Laval

Abstract

We introduce a new class of addition chains and show the numbers for which these chains are optimal satisfy the Scholz conjecture, precisely the inequality $$\iota(2^n-1)\leq n-1+\iota(n).$$

Metadata

Available format(s): PDF
Category: Foundations
Publication info: Preprint.
Keywords: Closed; complete
Contact author(s): thaga1 @ ulaval ca
History: 2025-05-12: approved; 2025-05-09: received; See all versions
Short URL: https://ia.cr/2025/833
License: CC BY

BibTeX

@misc{cryptoeprint:2025/833,
      author = {Theophilus Agama},
      title = {A note on closed addition chains and complete numbers},
      howpublished = {Cryptology {ePrint} Archive, Paper 2025/833},
      year = {2025},
      url = {https://eprint.iacr.org/2025/833}
}