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Unformatted text preview: * ) agree at 1 ,..., n . Indeed, this would say that the dierence of the two sides is a polynomial of degree less than n having n roots, which would force it to be the zero polynomial. By the product rule for derivatives, we have Q ( k ) = Y j 6 = k ( k j ) and by direct calculation Q ( z ) ( z k ) z = ` = jk . Now we evaluate each side of ( * ) at j to obtain: RHS : n X k =1 P ( k ) jk = P ( j ) LHS : P ( j ) Hence the RHS and LHS of ( * ) agree at each j and the proof is complete. 1...
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 Three '09
 Cong
 Math

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