let give F(x) = (1/(x^2 +1)) prove that ∃ P_n ∈ Z_n [x] / F^((n)) (x)= ((P_n (x))/((1+x^2 )^n )) find a relation of recurence between the P_n .prove that all roots of P


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Question Number 28364 by abdo imad last updated on 24/Jan/18

$l e t g i v e F (x) = \frac{1}{x^{2} + 1} p r o v e t h a t \exists P_{n} \in Z_{n} [x] /$ $F^{(n)} (x) = \frac{P_{n} (x)}{{(1 + x^{2})}^{n}} f i n d a r e l a t i o n o f r e c u r e n c e b e t w e e n$ $t h e P_{n} . p r o v e t h a t a l l r o o t s o f P_{n} a r e r e a l s a n d s m p l e s .$
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