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Fantezi Cebir => Fantezi Cebir => Konuyu başlatan: stuart clark - Şubat 13, 2013, 09:13:39 ös

Başlık: polynomial sum
Gönderen: stuart clark - Şubat 13, 2013, 09:13:39 ös

Consider the polynomial (http://latex.codecogs.com/gif.latex?$\bf{\displaystyle%20\bf{p(x)}%20=%20\prod_{r=0}^{10}\left(x^{2^{k}}+2^k\right)}$.). Then Coefficient of x²⁰¹² in p(x)

Başlık: Ynt: polynomial sum
Gönderen: senior - Şubat 14, 2013, 04:58:05 ös

2012 = 2¹⁰ + 2⁹ + 2⁸ + 2⁷ + 2⁶ + 2⁴ + 2³ + 2², so in the product we need these terms as power of x. The remaining parts will be multiplied with x²⁰¹² which yields 2⁵ * 2¹ * 2⁰ = 64

Başlık: Ynt: polynomial sum
Gönderen: stuart clark - Şubat 18, 2013, 07:45:17 ös

Thanks Moderator