2002 Cayley 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?

\textbf{(A)}\ 1\quad \textbf{(B)}\ 2\quad \textbf{(C)}\ 3\quad \textbf{(D)}\ 4\quad \textbf{(E)}\ 5

If there are no answer choices shown, enter a numerical answer.

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