MathDB

1. Baron Munchhausen was told that some polynomial

P(x)=a_{n} x^{n}+\ldots+a_{1} x+a_{0}

is such that

P(x)+P(-x)

has exactly 45 distinct real roots. Baron doesn't know the value of

n

. Nevertheless he claims that he can determine one of the coefficients

a_{n}, \ldots, a_{1}, a_{0}

(indicating its position and value). Isn't Baron mistaken? Boris Frenkin

Problem Statement