Find the number of positive integer solutions to x2−y2=2kx^2 - y^2 = 2^kx2−y2=2k for a fixed integer k>3k > 3k>3.
2k−1−12^{k-1}-12k−1−1
2k−2−12^{k-2}-12k−2−1
2k−22^{k-2}2k−2
None