preprints_ui: t93k7_v1
Data license: ODbL (database) & original licenses (content) · Data source: Open Science Framework
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| t93k7_v1 | On The Diophantine equation (x^n-1)(y^n-1)=z^n-1 | Using a variety of techniques, including the hypergeometric method of Thue and Siegel, as well as an assortment of gap principles, M . Bennett proved that the Diophantine equation (x^n-1 ) (y^n-1)=z^n-1 has only the solutions (x;y;z;n)=(-1;4;-5;3) and (4;-1;-5;3) in integers x;y;z and n with |z|>1 and n>2. We aim to prove them in very weak systems using elementary function of arithmetic (EFA), On a new, easy and simple, it's the combination of congruence and infinite descent of Fermat. | 2020-07-10T15:41:24.395042 | 2020-09-03T01:51:32.704383 | 2020-07-18T10:11:20.432967 | arabixiv | 0 | withdrawn | 1 | 1 | https://doi.org/10.31221/osf.io/t93k7 | No license | Diophantine equation; Infinite Descent of congruences | ["Diophantine equation", "Infinite Descent of congruences"] | Himane Djamel | [{"id": "bphc3", "name": "Himane Djamel", "index": 0, "orcid": null, "bibliographic": true}] | Himane Djamel | Physical Sciences and Mathematics; Mathematics; Number Theory | [{"id": "5a57d9d0076808000d815268", "text": "Physical Sciences and Mathematics"}, {"id": "5a57d9d2076808000d81528d", "text": "Mathematics"}, {"id": "5a57d9d4076808000d8152e1", "text": "Number Theory"}] | 0 | not_applicable | null | 2025-04-09T20:03:43.138214 |