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- W2092715653 abstract "Un m-uplet diophantien est un ensemble de m entiers naturels non nuls tel que le produit quelconque de deux d'entre eux augmente de 1 est un carre parfait. Dans cet article, nous nous interessons a certaines proprietes de courbes elliptiques d'equation du type y 2 = (ax + 1)(bx + 1)(cx + 1), ou {a,b,c} est un triplet diophantien. Nous considerons en particulier la courbe elliptique E k definie par l'equation y 2 = (F 2k x + 1)(F 2k+2 x + 1)(F 2k+4 x + 1), ou k ≥ 2 et F n designe le n-eme nombre de Fibonacci. Nous montrons que si le rang de E k est egal a 1, ou si k < 50, alors les points entiers sur E k sont donnes par (x,y) ∈ {(0,±1), (4F 2k+1 F 2k+2 F 2k+3 , ±(2F 2k+1 F 2k+2 - 1) × (2F 2 2k+2 + 1)(2F 2k+2 F 2k+3 + 1))}." @default.
- W2092715653 created "2016-06-24" @default.
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- W2092715653 date "2001-01-01" @default.
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- W2092715653 title "Diophantine $m$-tuples and elliptic curves" @default.
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- W2092715653 doi "https://doi.org/10.5802/jtnb.308" @default.
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