MathDB

Two polynomials of the same degree

A(x)=a_nx^n+ \cdots + a_1x+a_0

and

B(x)=b_nx^n+\cdots+b_1x+b_0

are called friends is the coefficients

b_0,b_1, \ldots, b_n

are a permutation of the coefficients

a_0,a_1, \ldots, a_n

P(x)

and

Q(x)

be two friendly polynomials with integer coefficients. If

P(16)=3^{2020}

, the smallest possible value of

|Q(3^{2020})|

P6