Given a positive integer n, find the pivot integer x such that:

- The sum of all elements between 1 and x inclusively equals the sum of all elements between x and n inclusively.
Return the pivot integer x. If no such integer exists, return -1. It is guaranteed that there will be at most one pivot index for the given input.

Solution

```
class Solution {
public int pivotInteger(int n) {
if(n==1) return 1;
for (int i = n - 1; i > 0; i--) {
if (((n * (n + 1)) / 2) - ((i * (i - 1)) / 2) == (i * (i + 1)) / 2)
return i;
}
return -1;
}
}
```

reference:

https://leetcode.com/problems/find-the-pivot-integer/

https://math.stackexchange.com/a/2713667/1053103

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