MathDB

All possible vertical lines

x = k

and horizontal lines

y = m

are drawn on the coordinate plane, where

k

and

m

are integers. Let's imagine that all these straight lines are black. A red straight line is also drawn, the equation of which is

19x+96y= c

. Let us denote by

M

the number of segments of different lengths formed on the red line when intersecting with the black ones.(The ends of each segment are the intersection points of the red and black lines. There are no such intersection points inside the segment.) What values can

M

take when

c

changes?

Problem Statement