Given an array nums containing n + 1 integers where each integer is between 1 and n (inclusive), prove that at least one duplicate number must exist. Assume that there is only one duplicate number, find the duplicate one.
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(n^{2}).
There is only one duplicate number in the array, but it could be repeated more than once.
Credits: Special thanks to @jianchao.li.fighter for adding this problem and creating all test cases.
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