On the approximation gain for abc-triples
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arXiv
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| Format: | Preprint |
| Published: |
2026
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| _version_ | 1866918327786405888 |
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| author | de Weger, Benne |
| author_facet | de Weger, Benne |
| contents | The concept of approximation gain was introduced recently by Müller and Taktikos for some abc-triples related to convergents of surds, where there is a relatively large gap between min{a,b,c} and max{a,b,c}. This note proposes a generalization of the concept to all abc-triples, with several variants. Extensive numerical computations are provided. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_08051 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | On the approximation gain for abc-triples de Weger, Benne Number Theory 11A99 (Primary), 11J25, 11Y65 (Secondary) The concept of approximation gain was introduced recently by Müller and Taktikos for some abc-triples related to convergents of surds, where there is a relatively large gap between min{a,b,c} and max{a,b,c}. This note proposes a generalization of the concept to all abc-triples, with several variants. Extensive numerical computations are provided. |
| title | On the approximation gain for abc-triples |
| topic | Number Theory 11A99 (Primary), 11J25, 11Y65 (Secondary) |
| url | https://arxiv.org/abs/2602.08051 |