Putnam 1951 A5
Source:
May 25, 2022
Putnam
Problem Statement
Consider in the plane the network of points having integral coordinates. For lines having rational slope show that:(i) the line passes through no points of the network or through infinitely many;(ii) there exists for each line a positive number having the property that no point of the network, except such as may be on the line, is closer to the line than the distance