Find the Duplicate Number

Medium

Given an array of integers nums containing n + 1 integers where each integer is in the range [1, n] inclusive.

There is only one repeated number in nums, return this repeated number.

You must solve the problem without modifying the array nums and uses only constant extra space.

Example 1:

Input: nums = [1,3,4,2,2]
Output: 2

Example 2:

Input: nums = [3,1,3,4,2]
Output: 3

Example 3:

Input: nums = [1,1]
Output: 1

Example 4:

Input: nums = [1,1,2]
Output: 1

Constraints:

1 <= n <= 105
nums.length == n + 1
1 <= nums[i] <= n

All the integers in nums appear only once except for precisely one integer which appears two or more times.

Follow up:

How can we prove that at least one duplicate number must exist in nums?

Can you solve the problem in linear runtime complexity?