An arbitrary number of squares whose sum, on excluding any one of them, is also a square
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866909599861309440 |
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| author | Choudhry, Ajai |
| author_facet | Choudhry, Ajai |
| contents | This paper is concerned with the problem of finding $n$ distinct squares such that, on excluding any one of them, the sum of the remaining $n-1$ squares is a square. While parametric solutions are known when $n=3$ and $n=4$, when $n > 4$, only a finite number of numerical solutions, found by computer trials, are known. In fact, efforts to find parametric solutions for $n > 4$ have so far been futile. In this paper we describe two methods of obtaining parametric solutions of the problem, and we apply these methods to get several parametric solutions when $n=5, 6, 7$ or $8$. We also indicate how parametric solutions may be obtained for larger values of $n$. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2505_01667 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | An arbitrary number of squares whose sum, on excluding any one of them, is also a square Choudhry, Ajai Number Theory 11D09 This paper is concerned with the problem of finding $n$ distinct squares such that, on excluding any one of them, the sum of the remaining $n-1$ squares is a square. While parametric solutions are known when $n=3$ and $n=4$, when $n > 4$, only a finite number of numerical solutions, found by computer trials, are known. In fact, efforts to find parametric solutions for $n > 4$ have so far been futile. In this paper we describe two methods of obtaining parametric solutions of the problem, and we apply these methods to get several parametric solutions when $n=5, 6, 7$ or $8$. We also indicate how parametric solutions may be obtained for larger values of $n$. |
| title | An arbitrary number of squares whose sum, on excluding any one of them, is also a square |
| topic | Number Theory 11D09 |
| url | https://arxiv.org/abs/2505.01667 |