Saved in:
| Main Author: | |
|---|---|
| Format: | Preprint |
| Published: |
2024
|
| Subjects: | |
| Online Access: | https://arxiv.org/abs/2411.19364 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866917043551338496 |
|---|---|
| author | Zhang, Pengcheng |
| author_facet | Zhang, Pengcheng |
| contents | The question of integer complexity asks about the minimal number of $1$'s that are needed to express a positive integer using only addition and multiplication (and parentheses). In this paper, we propose the notion of $l$-complexity of multiples of $l$, which specializes to integer complexity when $l=1$, prove several elementary results on $2$-complexity of even positive integers, and raise some interesting questions on $2$-complexity and in general $l$-complexity. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_19364 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | The 2-complexity of even positive integers Zhang, Pengcheng Number Theory The question of integer complexity asks about the minimal number of $1$'s that are needed to express a positive integer using only addition and multiplication (and parentheses). In this paper, we propose the notion of $l$-complexity of multiples of $l$, which specializes to integer complexity when $l=1$, prove several elementary results on $2$-complexity of even positive integers, and raise some interesting questions on $2$-complexity and in general $l$-complexity. |
| title | The 2-complexity of even positive integers |
| topic | Number Theory |
| url | https://arxiv.org/abs/2411.19364 |