An Elementary Approach For Sums Of Consecutive Cubes Being Prime Power Squares
Fuente:
arXiv
Saved in:
| Main Author: | |
|---|---|
| Format: | Preprint |
| Published: |
2024
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866929204649525248 |
|---|---|
| author | Akkuş, Atilla |
| author_facet | Akkuş, Atilla |
| contents | This paper proposes an elementary solution to a special case of finding all perfect squares that can be written as sum of consecutive integer cubes. It is shown that there are no non-trivial solutions if the perfect square is a prime power, i.e., it is divisible by two different primes if a non-trivial one exists. Solution mostly depends on $v_{p}(x)$ and general forms of Pythagorean triples. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_04664 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | An Elementary Approach For Sums Of Consecutive Cubes Being Prime Power Squares Akkuş, Atilla General Mathematics This paper proposes an elementary solution to a special case of finding all perfect squares that can be written as sum of consecutive integer cubes. It is shown that there are no non-trivial solutions if the perfect square is a prime power, i.e., it is divisible by two different primes if a non-trivial one exists. Solution mostly depends on $v_{p}(x)$ and general forms of Pythagorean triples. |
| title | An Elementary Approach For Sums Of Consecutive Cubes Being Prime Power Squares |
| topic | General Mathematics |
| url | https://arxiv.org/abs/2401.04664 |