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let-give-P-n-x-1-x-2-n-1-and-Q-n-x-k-0-n-1-x-2-k-prove-that-Q-n-divide-P-n-




Question Number 28313 by abdo imad last updated on 23/Jan/18
let give  P_n (x)= 1−x^2^(n+1)     and  Q_n (x)= Π_(k=0) ^n (1+x^2^k  )  prove that Q_(n )  divide P_n .
$${let}\:{give}\:\:{P}_{{n}} \left({x}\right)=\:\mathrm{1}−{x}^{\mathrm{2}^{{n}+\mathrm{1}} } \:\:\:{and}\:\:{Q}_{{n}} \left({x}\right)=\:\prod_{{k}=\mathrm{0}} ^{{n}} \left(\mathrm{1}+{x}^{\mathrm{2}^{{k}} } \right) \\ $$$${prove}\:{that}\:{Q}_{{n}\:} \:{divide}\:{P}_{{n}} . \\ $$

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