A note on the Diophantine equation (xᵏ-1)(yᵏ-1)²=zᵏ-1
We prove that, for k≥10, the Diophantine equation (xᵏ-1)(yᵏ-1)²=zᵏ-1 in positive integers x, y, z, k with z>1, has no solutions satisfying 1<x≤y or 1<y<x≤((yᵏ-1)ᵏ⁻²+1)^{1/k}.
Shranjeno v:
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| Format: | Artigo |
| Jezik: | Inglês |
| Izdano: |
"Prof. Marin Drinov" Publishing House of Bulgarian Academy of Sciences
2024-11-01
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| Serija: | Notes on Number Theory and Discrete Mathematics |
| Teme: | |
| Online dostop: | https://nntdm.net/papers/nntdm-30/NNTDM-30-4-825-831.pdf |
| Oznake: |
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