Divide-and-Conquer Exercise I need help on this question:
Given a sorted array of distinct integers A[1, . . . , n], you want to find out whether there is an index i for which A[i] = i. Give a divide-and-conquer algorithm that runs in time O(log n).

How I can proceed?
Thanks a lot!
Hint: Define $B[i] = A[i] - i$. What can you say about the array $B$? Use the fact that $A$ contains distinct integers.