The problem of finding three numbers such that the sum or difference of any two of them is a square number
Fuente:
arXiv
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| Autore principale: | |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866912548056465408 |
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| author | Tomita, Seiji |
| author_facet | Tomita, Seiji |
| contents | Euler explored the problem of finding three numbers such that the sum or difference of any two of them is a perfect square. He discovered a parametric solution represented by polynomials of degree 18 and identified the smallest of these solutions. Additionally, we derive two parametric solutions using the elliptic curve method and find all solutions within the range of $10^8$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2508_15781 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | The problem of finding three numbers such that the sum or difference of any two of them is a square number Tomita, Seiji General Mathematics Euler explored the problem of finding three numbers such that the sum or difference of any two of them is a perfect square. He discovered a parametric solution represented by polynomials of degree 18 and identified the smallest of these solutions. Additionally, we derive two parametric solutions using the elliptic curve method and find all solutions within the range of $10^8$. |
| title | The problem of finding three numbers such that the sum or difference of any two of them is a square number |
| topic | General Mathematics |
| url | https://arxiv.org/abs/2508.15781 |