Problem:
A line passes through and . How many other points with integer coordinates are on the line and strictly between and
Answer Choices:
A.
B.
C.
D.
E.
Solution:
The slope of the line is
so all points on the line have the form . Such a point has integer coordinates if and only if is an integer, and the point is strictly between and if and only if . Thus there are points with the required property.
The problems on this page are the property of the MAA's American Mathematics Competitions