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smc

number theory senior

Problem

A line passes through and . How many other points with integer coordinates are on the line and strictly between and ?
(A)
(B)
(C)
(D)
Solution
For convenience's sake, we can transform to the origin and to (this does not change the problem). The line has the equation . The coordinates are integers if , so the values of are , with a total of coordinates.
Final answer
D