Problem: Let be a positive integer and let the lines and intersect in a point whose coordinates are integers. Then can be:
Answer Choices:
A. 4 only
B. 5 only
C. 6 only
D. 7 only
E. one of the integers and one other positive integer
Solution:
, with integral and integral. It is easy to see that must be even. Try in turn. Neither nor produce an integral but for , we have . Since two straight lines can intersect in at most one point (these lines do not coincide), is the only possible value.