Lattice point
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A lattice point is a point in a Cartesian coordinate system such that both its 
- and 
-coordinates are integers. A lattice point is a point at the intersection of two or more grid lines in a regularly spaced array of points, which is a point lattice. In a plane, point lattices can be constructed having unit cells in the shape of a square, rectangle, hexagon, and other shapes. If not specified, a point lattice is usually a point in a square array.
Example
A point lattice is constructed by plotting all of the points 
such that 
and 
are positive integers. How many points in the point lattice lie on the line 
?
Solution
Notice that 
. So, 
and 
are the only such points, giving us 
points.
~advanture
