Find the single number that duplicates one or more times

Find the single number that duplicates one or more times in an array in O(1) space and O(n) time without modifying the array

Note:
You must not modify the array (assume the array is read only).
You must use only constant, O(1) extra space.
Your runtime complexity should be less than O(n2).
There is only one duplicate number in the array, but it could be repeated more than once.

Search first occurrence of a duplicated element in a sorted array

Given an array of integer with duplicated elements. Find the first occurrence of a given number in the array.

For example: A = [1, 1, 1, 2, 2, 3, 3, 3, 4]. So, first occurrence of 2 is in index 3, first occurrence of 4 is in index 8.