Polinom

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Vlad Matei
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Joined: Wed Sep 26, 2007 6:44 pm
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Polinom

Post by Vlad Matei »

Un polinom \( P\in \mathbb{Z}[X] \) este numit "special" daca exista \( f_{1},...,f_{k}\in \mathbb{Z}[X] \) (pe \( k \) il putem alege) astfel incat \( \displaystyle P=f_{1}^3+...+f_{k}^3 \).
a) Este polinomul \( 3X+X^7 \) special?
b) Este polinomul \( 3X+3X^{7}+3X^{2008} \) special?

Zhautykov Olympiad 2008
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