MathDB

Let

P(x)

and

Q(x)

be two polynomials with integer coefficients, such that no nonconstant polynomial with rational coefficients divides both

P(x)

and

Q(x).

Suppose that for every positive integer

n

the integers

P(n)

and

Q(n)

are positive, and

2^{Q(n)}-1

divides

3^{P(n)}-1.

Prove that

Q(x)

is a constant polynomial.
Proposed by Oleksiy Klurman, Ukraine

Problem Statement