For each polynomial Q(x) let M(Q) be the set of non-negative integers x with 0<Q(x)<2004. We consider polynomials Pn(x) of the form
Pn(x)=xn+a1⋅xn−1+…+an−1⋅x+1
with coefficients ai∈{±1} for i=1,2,…,n−1.
For each n=3k,k>0 determine:
a.) mn which represents the maximum of elements in M(Pn) for all such polynomials Pn(x)
b.) all polynomials Pn(x) for which ∣M(Pn)∣=mn. algebrapolynomialalgebra unsolved