Home Competitions ILL 1978 Problem 31
Let the polynomials
P ( x ) = x n + a n − 1 x n − 1 + ⋯ + a 1 x + a 0 , P(x) = x^n + a_{n-1}x^{n-1 }+ \cdots + a_1x + a_0, P ( x ) = x n + a n − 1 x n − 1 + ⋯ + a 1 x + a 0 , Q ( x ) = x m + b m − 1 x m − 1 + ⋯ + b 1 x + b 0 , Q(x) = x^m + b_{m-1}x^{m-1} + \cdots + b_1x + b_0, Q ( x ) = x m + b m − 1 x m − 1 + ⋯ + b 1 x + b 0 , P ( x ) 2 = ( x 2 − 1 ) Q ( x ) 2 + 1 P(x)^2 = (x^2 - 1)Q(x)^2 + 1 P ( x ) 2 = ( x 2 − 1 ) Q ( x ) 2 + 1 P ′ ( x ) = n Q ( x ) . P'(x) = nQ(x). P ′ ( x ) = n Q ( x ) .
Dataset text AI-MO AoPS . Quoted with source.
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