Problem 52789. Easy Sequences 26: Prime-Integer Line Segments

Ramon Villamangca

8 solvers

1 likes

Solve

Solve Later

At the first quadrant in the -plane, you are asked to construct a line segment with the following specifications:
Select a prime point along the x-axis. 
Select an integer point along the y-axis. 
Connect these points to form a line segment. 
How many line segments, with the abovementioned specifications, can be constructed that pass through a given point ? 
For example, in the figure below, it is shown that 2 such lines pass through the point , with lines connecting prime points  and  to integer points  and , respectively. It can be proven that these are the only line segments, drawn as specified, that pass through .
                                           
NOTE: It is possible that no line segments, as specified, pass through a given point.