Integral Points
Source: 1986 National High School Mathematics League, Exam Two, Problem 3
February 24, 2020
calculusintegration
Problem Statement
In rectangular coordinate system, define that if and only if both -axis and -axis of a point are integers, we call it integral point. Please color all intengral points in white, red and black, satisfying:
(1) Points in every color appear on infinitely many lines that are parallel to -axis.
(2) For any white point , red point , black point , we can find another red point , such that is a parallelogram.