A line in Euclidean geometry is the set of points in a plane determined by two distinct points; it is the shortest path between any two of its points. A line contains infinitely many—indeed, uncountably many—points. In a given coordinate system, it can be characterized by a linear equation in two real variables, x and y, where the ordered pair (x, y) gives the coordinates of a point on the line.
Special points
In discrete geometry, we are interested in particular points on the line: those with integer coordinates, which we shall call integer points from now on.
Consider the following problem:
Given n collinear points in the plane (n ≥ 2), find all the integer points, if any, that lie on the same line as these n points.
