MathDB

We call polynomials

A(x) = a_n x^n +. . .+a_1 x+a_0

and

B(x) = b_m x^m +. . .+b_1 x+b_0

(

a_n b_m \neq 0

) similar if the following conditions hold:

(i)

n = m

;

(ii)

There is a permutation

\pi

of the set

\{ 0, 1, . . . , n\}

such that

b_i = a_{\pi (i)}

for each

i \in {0, 1, . . . , n}

. Let

P(x)

and

Q(x)

be similar polynomials with integer coefficients. Given that

P(16) = 3^{2012}

, find the smallest possible value of

|Q(3^{2012})|

.
Proposed by Milos Milosavljevic

Problem Statement