J'ai aussi ces tableaux des quotients et des restes pour n et p variant de 1 à 10 :
Cliquez pour afficherCode:Tableau du quotient de : t(n, p) = (3^n - 2^n)/(2^(n+p) - 3^n) +-----------------------------------------------------------------------------------------------------------------------------------------+ | | n = 1 | n = 2 | n = 3 | n = 4 | n = 5 | n = 6 | n = 7 | n = 8 | n = 9 | n = 10| |-----------------------------------------------------------------------------------------------------------------------------------------| |p = 0 | -1.000e+00 | -1.000e+00 | -1.000e+00 | -1.000e+00 | -1.000e+00 | -1.000e+00 | -1.000e+00 | -1.000e+00 | -1.000e+00 | -1.000e+00| |p = 1 | 1.000e+00 | -5.000e+00 | -1.727e+00 | -1.327e+00 | -1.179e+00 | -1.106e+00 | -1.066e+00 | -1.042e+00 | -1.027e+00 | -1.018e+00| |p = 2 | 2.000e-01 | 7.143e-01 | 3.800e+00 | -3.824e+00 | -1.835e+00 | -1.406e+00 | -1.229e+00 | -1.139e+00 | -1.087e+00 | -1.056e+00| |p = 3 | 7.692e-02 | 2.174e-01 | 5.135e-01 | 1.383e+00 | 1.623e+01 | -3.065e+00 | -1.770e+00 | -1.397e+00 | -1.230e+00 | -1.141e+00| |p = 4 | 3.448e-02 | 9.091e-02 | 1.881e-01 | 3.714e-01 | 7.844e-01 | 2.254e+00 | -1.481e+01 | -2.558e+00 | -1.668e+00 | -1.360e+00| |p = 5 | 1.639e-02 | 4.202e-02 | 8.297e-02 | 1.508e-01 | 2.702e-01 | 5.042e-01 | 1.079e+00 | 3.866e+00 | -5.811e+00 | -2.208e+00| |p = 6 | 8.000e-03 | 2.024e-02 | 3.918e-02 | 6.893e-02 | 1.169e-01 | 1.975e-01 | 3.429e-01 | 6.419e-01 | 1.465e+00 | 8.945e+00| |p = 7 | 3.953e-03 | 9.940e-03 | 1.906e-02 | 3.305e-02 | 5.476e-02 | 8.911e-02 | 1.450e-01 | 2.406e-01 | 4.181e-01 | 8.056e-01| |p = 8 | 1.965e-03 | 4.926e-03 | 9.401e-03 | 1.619e-02 | 2.654e-02 | 4.248e-02 | 6.733e-02 | 1.069e-01 | 1.721e-01 | 2.857e-01| |p = 9 | 9.794e-04 | 2.452e-03 | 4.669e-03 | 8.014e-03 | 1.307e-02 | 2.076e-02 | 3.250e-02 | 5.064e-02 | 7.907e-02 | 1.247e-01| |p = 10 | 4.890e-04 | 1.223e-03 | 2.327e-03 | 3.987e-03 | 6.487e-03 | 1.026e-02 | 1.598e-02 | 2.467e-02 | 3.799e-02 | 5.864e-02| +-----------------------------------------------------------------------------------------------------------------------------------------+ Tableau du reste de : t(n, p) = (3^n - 2^n)/(2^(n+p) - 3^n) +-----------------------------------------------------------------------------------------------------------------------------------------+ | | n = 1 | n = 2 | n = 3 | n = 4 | n = 5 | n = 6 | n = 7 | n = 8 | n = 9 | n = 10| |-----------------------------------------------------------------------------------------------------------------------------------------| |p = 0 | 0.000e+00 | 0.000e+00 | 0.000e+00 | 0.000e+00 | 0.000e+00 | 0.000e+00 | 0.000e+00 | 0.000e+00 | 0.000e+00 | 0.000e+00| |p = 1 | 0.000e+00 | 0.000e+00 | -3.000e+00 | -3.300e+01 | -1.470e+02 | -5.370e+02 | -1.803e+03 | -5.793e+03 | -1.815e+04 | -5.598e+04| |p = 2 | 1.000e+00 | 5.000e+00 | 4.000e+00 | -3.000e+00 | -1.900e+01 | -2.810e+02 | -1.291e+03 | -4.769e+03 | -1.610e+04 | -5.188e+04| |p = 3 | 1.000e+00 | 5.000e+00 | 1.900e+01 | 1.800e+01 | 3.000e+00 | -2.030e+02 | -2.670e+02 | -2.721e+03 | -1.200e+04 | -4.369e+04| |p = 4 | 1.000e+00 | 5.000e+00 | 1.900e+01 | 6.500e+01 | 2.110e+02 | 7.500e+01 | -2.600e+01 | -1.090e+03 | -3.811e+03 | -2.730e+04| |p = 5 | 1.000e+00 | 5.000e+00 | 1.900e+01 | 6.500e+01 | 2.110e+02 | 6.650e+02 | 1.500e+02 | 1.412e+03 | -6.230e+02 | -2.082e+04| |p = 6 | 1.000e+00 | 5.000e+00 | 1.900e+01 | 6.500e+01 | 2.110e+02 | 6.650e+02 | 2.059e+03 | 6.305e+03 | 6.086e+03 | 6.129e+03| |p = 7 | 1.000e+00 | 5.000e+00 | 1.900e+01 | 6.500e+01 | 2.110e+02 | 6.650e+02 | 2.059e+03 | 6.305e+03 | 1.917e+04 | 5.802e+04| |p = 8 | 1.000e+00 | 5.000e+00 | 1.900e+01 | 6.500e+01 | 2.110e+02 | 6.650e+02 | 2.059e+03 | 6.305e+03 | 1.917e+04 | 5.802e+04| |p = 9 | 1.000e+00 | 5.000e+00 | 1.900e+01 | 6.500e+01 | 2.110e+02 | 6.650e+02 | 2.059e+03 | 6.305e+03 | 1.917e+04 | 5.802e+04| |p = 10 | 1.000e+00 | 5.000e+00 | 1.900e+01 | 6.500e+01 | 2.110e+02 | 6.650e+02 | 2.059e+03 | 6.305e+03 | 1.917e+04 | 5.802e+04| +-----------------------------------------------------------------------------------------------------------------------------------------+
Ils semblent indiquer que la seule valeur de p intéressante est l'entier qui suit directement la racine du dénominateur appelée p0, alors p= int(p0) + 1 est la seule valeurs qui nous intéresse.
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