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-n-are-reals-and-smples-

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 .