CAYLEY 2002 Problem 25

A lattice\:point is a point (x,y) where both x and y are integers For how many different integer values of k will the two lines kx-5y+7=0 and k^2x-5y+1=0 intersect at a lattice point?

Answer Choices
A. 1
B. 2
C. 3
D. 4
E. 5