Find Duplicate in Range 0 and n-1

Code

#include <stdio.h>

int find_duplicate(int arr[], int n) {
    long long sum = 0, sumSq = 0;

    for (int i = 0; i < n; i++) {
        sum += arr[i];
        sumSq += 1LL * arr[i] * arr[i];
    }

    long long expectedSum = 1LL * n * (n - 1) / 2;                 // sum 0..n-1
    long long expectedSumSq = 1LL * (n - 1) * n * (2LL * n - 1) / 6; // sum of squares 0..n-1

    long long diff = sum - expectedSum;        // D - M
    long long diff2 = sumSq - expectedSumSq;   // D^2 - M^2

    long long dPlusM = diff2 / diff;           // D + M (chia hết)
    long long duplicate = (diff + dPlusM) / 2; // D

    return (int)duplicate;;
}

int main() {
    int n;
    scanf("%d", &n);

    int arr[100];
    for (int i = 0; i < n; i++) scanf("%d", &arr[i]);

    int result = find_duplicate(arr, n);
    printf("%d", result);
    return 0;
}

Solving Approach