# If possible, use binary search to find an element in sorted array

Given sorted array $$A[1..n]$$, we want to find an element such that, $$A[i]=i^2$$,Can we use binary search to find such a element?

My Attempt: initially, I read this link, but I can't understand the comments for why we can't find that element in $$O(\log n)$$. Any hint be appreciated.

No. Let's define an array $$B$$ as $$B[i] = i^2 - 1$$. Clearly it has no solution, but it is sorted.
Now I define $$A$$ to be a copy of $$B$$, with exactly one element, $$A[k]$$ incremented by one. This array is still easily seen to be sorted, but there's no way to find out which $$k$$ I used to increment a single element other than scanning the complete array. After all, if you inspect $$n - 1$$ indices of this array, I could've chosen $$k$$ as the single index you didn't look at.