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Check if a given pair of Numbers are Betrothed numbers or not
• Difficulty Level : Easy
• Last Updated : 16 Apr, 2021

Given two positive numbers N and M, the task is to check whether the given pairs of numbers (N, M) form a Betrothed Numbers or not.
Examples:

Input: N = 48, M = 75
Output: Yes
Explanation:
The proper divisors of 48 are 1, 2, 3, 4, 6, 8, 12, 16, 24
Sum of proper divisors of 48 is 75(sum1
The proper divisors of 75 are 1, 3, 5, 15, 25
Sum of proper divisors of 48 is 49(sum2
Since sum2 = N + 1, therefore the given pairs form berothered numbers.
Input: N = 95, M = 55
Output: No
Explanation:
The proper divisors of 95 are 1, 5, 19
Sum of proper divisors of 48 is 25(sum1
The proper divisors of 55 are 1, 5, 11
Sum of proper divisors of 48 is 17(sum2
Since Neither sum2 is equals N + 1 nor sum1 is equals to M + 1, therefore the given pairs doesn’t form berothered numbers.

Approach:

1. Find the sum of proper divisors of the given numbers N and M.
2. If sum of proper divisors of N is equals to M + 1 or sum of proper divisors of M is equals to N + 1 then the given pairs form a Betrothed Numbers.
3. Else it doen’t forms a pair of Betrothed Numbers.

Below is the implementation of the above approach:

## C++

 `// C++ program for the above approach``#include ``using` `namespace` `std;` `// Function to check whether N is``// Perfect Square or not``bool` `isPerfectSquare(``int` `N)``{` `    ``// Find sqrt``    ``double` `sr = ``sqrt``(N);` `    ``return` `(sr - ``floor``(sr)) == 0;``}` `// Function to check whether the given``// pairs of numbers is Betrothed Numbers``// or not``void` `BetrothedNumbers(``int` `n, ``int` `m)``{``    ``int` `Sum1 = 1;``    ``int` `Sum2 = 1;` `    ``// For finding the sum of all the``    ``// divisors of first number n``    ``for` `(``int` `i = 2; i <= ``sqrt``(n); i++) {``        ``if` `(n % i == 0) {``            ``Sum1 += i``                    ``+ (isPerfectSquare(n)``                           ``? 0``                           ``: n / i);``        ``}``    ``}` `    ``// For finding the sum of all the``    ``// divisors of second number m``    ``for` `(``int` `i = 2; i <= ``sqrt``(m); i++) {``        ``if` `(m % i == 0) {``            ``Sum2 += i``                    ``+ (isPerfectSquare(m)``                           ``? 0``                           ``: m / i);``        ``}``    ``}` `    ``if` `((n + 1 == Sum2)``        ``&& (m + 1 == Sum1)) {``        ``cout << ``"YES"` `<< endl;``    ``}``    ``else` `{``        ``cout << ``"NO"` `<< endl;``    ``}``}` `// Driver Code``int` `main()``{``    ``int` `N = 9504;``    ``int` `M = 20734;` `    ``// Function Call``    ``BetrothedNumbers(N, M);` `    ``return` `0;``}`

## Java

 `// Java program for the above approach``class` `GFG{`` ` `// Function to check whether N is``// Perfect Square or not``static` `boolean` `isPerfectSquare(``int` `N)``{`` ` `    ``// Find sqrt``    ``double` `sr = Math.sqrt(N);`` ` `    ``return` `(sr - Math.floor(sr)) == ``0``;``}`` ` `// Function to check whether the given``// pairs of numbers is Betrothed Numbers``// or not``static` `void` `BetrothedNumbers(``int` `n, ``int` `m)``{``    ``int` `Sum1 = ``1``;``    ``int` `Sum2 = ``1``;`` ` `    ``// For finding the sum of all the``    ``// divisors of first number n``    ``for` `(``int` `i = ``2``; i <= Math.sqrt(n); i++) {``        ``if` `(n % i == ``0``) {``            ``Sum1 += i``                    ``+ (isPerfectSquare(n)``                           ``? ``0``                           ``: n / i);``        ``}``    ``}`` ` `    ``// For finding the sum of all the``    ``// divisors of second number m``    ``for` `(``int` `i = ``2``; i <= Math.sqrt(m); i++) {``        ``if` `(m % i == ``0``) {``            ``Sum2 += i``                    ``+ (isPerfectSquare(m)``                           ``? ``0``                           ``: m / i);``        ``}``    ``}`` ` `    ``if` `((n + ``1` `== Sum2)``        ``&& (m + ``1` `== Sum1)) {``        ``System.out.print(``"YES"` `+``"\n"``);``    ``}``    ``else` `{``        ``System.out.print(``"NO"` `+``"\n"``);``    ``}``}`` ` `// Driver Code``public` `static` `void` `main(String[] args)``{``    ``int` `N = ``9504``;``    ``int` `M = ``20734``;`` ` `    ``// Function Call``    ``BetrothedNumbers(N, M);``}``}` `// This code is contributed by 29AjayKumar`

## Python3

 `# Python3 program for the above approach``from` `math ``import` `sqrt,floor` `# Function to check whether N is``# Perfect Square or not``def` `isPerfectSquare(N):``    ``# Find sqrt``    ``sr ``=` `sqrt(N)` `    ``return` `(sr ``-` `floor(sr)) ``=``=` `0` `# Function to check whether the given``# pairs of numbers is Betrothed Numbers``# or not``def` `BetrothedNumbers(n,m):``    ``Sum1 ``=` `1``    ``Sum2 ``=` `1` `    ``# For finding the sum of all the``    ``# divisors of first number n``    ``for` `i ``in` `range``(``2``,``int``(sqrt(n))``+``1``,``1``):``        ``if` `(n ``%` `i ``=``=` `0``):``            ``if` `(isPerfectSquare(n)):``                ``Sum1 ``+``=` `i``            ``else``:``                ``Sum1 ``+``=` `i ``+` `n``/``i` `    ``# For finding the sum of all the``    ``# divisors of second number m``    ``for` `i ``in` `range``(``2``,``int``(sqrt(m))``+``1``,``1``):``        ``if` `(m ``%` `i ``=``=` `0``):``            ``if` `(isPerfectSquare(m)):``                ``Sum2 ``+``=` `i``            ``else``:``                ``Sum2 ``+``=` `i ``+` `(m ``/` `i)` `    ``if` `((n ``+` `1` `=``=` `Sum2) ``and` `(m ``+` `1` `=``=` `Sum1)):``        ``print``(``"YES"``)   ``    ``else``:``        ``print``(``"NO"``)` `# Driver Code``if` `__name__ ``=``=` `'__main__'``:``    ``N ``=` `9504``    ``M ``=` `20734` `    ``# Function Call``    ``BetrothedNumbers(N, M)` `# This code is contributed by Surendra_Gangwar`

## C#

 `// C# program for the above approach``using` `System;` `class` `GFG{` `// Function to check whether N is``// perfect square or not``static` `bool` `isPerfectSquare(``int` `N)``{` `    ``// Find sqrt``    ``double` `sr = Math.Sqrt(N);` `    ``return` `(sr - Math.Floor(sr)) == 0;``}` `// Function to check whether the given``// pairs of numbers is Betrothed numbers``// or not``static` `void` `BetrothedNumbers(``int` `n, ``int` `m)``{``    ``int` `Sum1 = 1;``    ``int` `Sum2 = 1;` `    ``// For finding the sum of all the``    ``// divisors of first number n``    ``for``(``int` `i = 2; i <= Math.Sqrt(n); i++)``    ``{``       ``if` `(n % i == 0)``       ``{``           ``Sum1 += i + (isPerfectSquare(n) ?``                                 ``0 : n / i);``       ``}``    ``}` `    ``// For finding the sum of all the``    ``// divisors of second number m``    ``for``(``int` `i = 2; i <= Math.Sqrt(m); i++)``    ``{``       ``if` `(m % i == 0)``       ``{``           ``Sum2 += i + (isPerfectSquare(m) ?``                                 ``0 : m / i);``       ``}``    ``}` `    ``if` `((n + 1 == Sum2) && (m + 1 == Sum1))``    ``{``        ``Console.Write(``"YES"` `+ ``"\n"``);``    ``}``    ``else``    ``{``        ``Console.Write(``"NO"` `+ ``"\n"``);``    ``}``}` `// Driver Code``public` `static` `void` `Main(String[] args)``{``    ``int` `N = 9504;``    ``int` `M = 20734;` `    ``// Function Call``    ``BetrothedNumbers(N, M);``}``}` `// This code is contributed by Rajput-Ji`

## Javascript

 ``
Output:
`NO`

Time Complexity: O(√N + √M)

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