#### Check Amicable Pair

```/**
* @file
* @brief A C++ Program to check whether a pair of numbers is an [amicable
* pair](https://en.wikipedia.org/wiki/Amicable_numbers) or not.
*
* @details
* An Amicable Pair is two positive integers such that the sum of the proper
* divisor for each number is equal to the other number.
*
* @note Remember that a proper divisor is any positive whole number that
* divides into a selected number, apart from the selected number itself, and
* returns a positive integer. for example 1, 2 and  5 are all proper divisors
* of 10.
*
* @author [iamnambiar](https://github.com/iamnambiar)
*/
#include <cassert>   /// for assert
#include <iostream>  /// for IO operations

/**
* @brief Mathematical algorithms
* @namespace
*/
namespace math {
/**
* @brief Function to calculate the sum of all the proper divisor
* of an integer.
* @param num selected number.
* @return Sum of the proper divisor of the number.
*/
int sum_of_divisor(int num) {
// Variable to store the sum of all proper divisors.
int sum = 1;
// Below loop condition helps to reduce Time complexity by a factor of
// square root of the number.
for (int div = 2; div * div <= num; ++div) {
// Check 'div' is divisor of 'num'.
if (num % div == 0) {
// If both divisor are same, add once to 'sum'
if (div == (num / div)) {
sum += div;
} else {
// If both divisor are not the same, add both to 'sum'.
sum += (div + (num / div));
}
}
}
return sum;
}

/**
* @brief Function to check whether the pair is amicable or not.
* @param x First number.
* @param y Second number.
* @return `true` if the pair is amicable
* @return `false` if the pair is not amicable
*/
bool are_amicable(int x, int y) {
return (sum_of_divisor(x) == y) && (sum_of_divisor(y) == x);
}
}  // namespace math

/**
* @brief Self-test implementations
* @returns void
*/
static void tests() {
assert(math::are_amicable(220, 284) == true);
assert(math::are_amicable(6368, 6232) == true);
assert(math::are_amicable(458, 232) == false);
assert(math::are_amicable(17296, 18416) == true);
assert(math::are_amicable(18416, 17296) == true);

std::cout << "All tests have successfully passed!" << std::endl;
}

/**
* @brief Main function
* @returns 0 on exit
*/
int main() {
tests();  // perform self-tests implementations
return 0;
}
```