Prove by induction. In your inductive step, you will need to use the result k² > 2k+1 for integers k > 4 in order to retrieve the perfect square.
This result can be proven in a number of ways. Perhaps the shortest approach is as follows:
k > 4
k² > 4k
k² > 2k + 2k > 2k + 1 (since 2k > 8 > 1)