Formatted question description: https://leetcode.ca/all/2177.html

# 2177. Find Three Consecutive Integers That Sum to a Given Number (Medium)

Given an integer num, return three consecutive integers (as a sorted array) that sum to num. If num cannot be expressed as the sum of three consecutive integers, return an empty array.

Example 1:

Input: num = 33
Output: [10,11,12]
Explanation: 33 can be expressed as 10 + 11 + 12 = 33.
10, 11, 12 are 3 consecutive integers, so we return [10, 11, 12].


Example 2:

Input: num = 4
Output: []
Explanation: There is no way to express 4 as the sum of 3 consecutive integers.


Constraints:

• 0 <= num <= 1015

Similar Questions:

## Solution 1. Math

Let x be the first number of the 3 consecutive numbers. Then num = x + x + 1 + x + 2 = 3 * x + 3. Since x is an integer, num must be multiple of 3, and x = num / 3 - 1.

// OJ: https://leetcode.com/problems/find-three-consecutive-integers-that-sum-to-a-given-number/

// Time: O(1)
// Space: O(1)
class Solution {
public:
vector<long long> sumOfThree(long long num) {
if (num % 3) return {};
long x = num / 3 - 1;
return {x, x + 1, x + 2};
}
};


Or one-liner

// OJ: https://leetcode.com/problems/find-three-consecutive-integers-that-sum-to-a-given-number/

// Time: O(1)
// Space: O(1)
class Solution {
public:
vector<long long> sumOfThree(long long num) {
return num % 3 ? vector<long long>{} : vector<long long>{num / 3 - 1, num / 3, num / 3 + 1};
}
};


## Discuss

https://leetcode.com/problems/find-three-consecutive-integers-that-sum-to-a-given-number/discuss/1783380/C%2B%2B-Math-one-liner