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polynomials - $\mathbb{F}_{7}$ 上の奇妙な多項式列
$\mathbb{F} {7}[X]$ で $P=X^{10} +5X^{5}+1$ および $Q=5X^{8}+6X^{3}$ とする。ユークリッド除算 $$U {2i}PX^{4}U_{2i-1}^{7}=4.3^{2i-1}Q$$ $$U_{2i+1}のこの奇妙な関係を証明する方法PX^{-4}U_{2i}^{7}=4.3^{2i}Q/X$$ with $U_{1}=X^{2}$?$U_{2i}=[X^ {4}U_{2i-1}^{7}/P]$ および $U_{2i+1}=[X^{-4}U_{2i}^{7}/P]$.