Problem:
Let be a positive integer. If the equation has solutions in positive integers and , then must be either
Answer Choices:
A. or
B. or
C. or
D. or
E. or
Solution:
Because is positive, solving is equivalent to solving in positive integers and . The number of solutions to this inequality is the number of lattice points inside the triangle in the first quadrant formed by the coordinate axes and the line . Since must be chosen so that there are exactly lattice points on the line in . That is, must be inside but is on or outside . Hence , so that is or .