When you take the nth root of something, you introduce n solutions.
For example, z^4 = 625 has roots z = 5w where w is the fourth root of unity. That is to say z = 5,-5,5i, -5i
Z-2)^2015 = 2^2017
Or, (Z-2) = (2^(2017/2015)) w
Or, Z = 2^(2017/2015) w + 2
The second line takes the 2015th root on both sides, wouldn't that introduce 2015 solutions?