| viXra.org > Number Theory > viXra:1509.0091 |
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| viXra.org > Number Theory > viXra:1509.0091 |
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Number Theory |
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Authors: Abdelmajid Ben Hadj Salem
En 1997, Andrew Beal avait annoncé la conjecture suivante: Soient A, B,C, m,n, et l des entiers positifs avec m,n,l >2. Si A^m + ^n = C^l alors A, B,et C ont un facteur commun. Nous commençons par construire le polynôme P(x)=(x-A^m)(x-B^n)(x+C^l)=x^3-px+q avec p,q des entiers qui dépendent de A^m,B^n et C^l. Nous résolvons l'équation x^3-px+q=0 et nous obtenons les trois racines x_1,x_2,x_3 comme fonctions de p,q et d'un paramètre µ. Comme A^m,B^n,-C^l sont les seules racines de x^3-px+q=0, nous discutons les conditions pour que x_1,x_2,x_3 soient des entiers.
Comments: 25 Pages. French translation of the English version of the paper ' An Elementary Proof of the BEAL Conjecture. La version anglaise est soumise au journal Integers. Bienvenue à vos commentaires.
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[v1] 2015-09-08 05:04:36
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