Find the Duplicate Number

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.

public class Solution {
    public int findDuplicate(int[] nums) {

        int n = nums.length;

        int slow = 0;
        int fast = 0;

        do{
            slow = nums[slow];
            fast = nums[nums[fast]];
        }while(slow != fast);

        slow = 0;
        while(slow != fast){

            slow = nums[slow];
            fast = nums[fast];
        }

        return slow;
    }
}

public class Solution {
    public int findDuplicate(int[] nums) {

        int n = nums.length;

        int slow = n;
        int fast = n;

        do{
            slow = nums[slow - 1];
            fast = nums[nums[fast - 1] - 1];
        }while(slow != fast);

        slow = n;

        while(slow != fast){
            slow = nums[slow - 1];
            fast = nums[fast - 1];
        }

        return slow;
    }
}