MathDB

Let

P(x, y)

and

Q(x, y)

be polynomials in two variables with integer coefficients. The sequences of integers

a_0, a_1,\ldots

and

b_0, b_1,\ldots

satisfy a_{n+1}=P(a_n,b_n), b_{n+1}=Q(a_n,b_n)for all

n\geqslant 0

. Let

m_n

be the number of integer points of the coordinate plane, lying strictly inside the segment with endpoints

(a_n,b_n)

and

(a_{n+1},b_{n+1})

. Prove that the sequence

m_0,m_1,\ldots

is non-decreasing.

Problem Statement