Seven squares from three numbers
Fuente:
arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2026
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| Subjects: | |
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| _version_ | 1866913020819537920 |
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| author | Dujella, Andrej Kazalicki, Matija Petričević, Vinko |
| author_facet | Dujella, Andrej Kazalicki, Matija Petričević, Vinko |
| contents | We study triples {a,b,c} of distinct nonzero rational numbers such that a+1,b+1,c+1,ab+1,ac+1,bc+1 and abc+1 are all perfect squares. We prove that there exist infinitely many such triples. In contrast, we show that no triple of positive integers has this property. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_08729 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Seven squares from three numbers Dujella, Andrej Kazalicki, Matija Petričević, Vinko Number Theory We study triples {a,b,c} of distinct nonzero rational numbers such that a+1,b+1,c+1,ab+1,ac+1,bc+1 and abc+1 are all perfect squares. We prove that there exist infinitely many such triples. In contrast, we show that no triple of positive integers has this property. |
| title | Seven squares from three numbers |
| topic | Number Theory |
| url | https://arxiv.org/abs/2604.08729 |