# Pair with min absolute difference and whose product is N+1 or N+2

Given an integer N, the task is to find a pair such that whose product is N + 1 or N + 2 and absolute difference of the pair is minimum.

Examples:

Input: N = 8
Output: 3, 3
Explanation: 3 * 3 = 8 + 1
Input: N = 123
Output: 5, 25
Explanation: 5 * 25 = 123 + 2

Approach: The idea is to Iterate a loop with a loop variable i from sqrt(N+2) to 1, and check the following conditions:

• if (n + 1) % i = 0, then we will print the pair (i, (n + 1) / i).
• if (n + 2) % i = 0, then we will print the pair (i, (n + 2) / i).
• The first pair printed will be the pair with minimum absolute difference.

Below is the implementation of the above approach:

## C++

 `// C++ program for the above approach` `#include ` `using` `namespace` `std;`   `// Function to print pair (a, b)` `// such that a*b=N+1 or N+2` `void` `closestDivisors(``int` `n)` `{` `    ``// Loop to iterate over the` `    ``// desired possible values` `    ``for` `(``int` `i = ``sqrt``(n + 2);` `         ``i > 0; i--) {`   `        ``// Check for condition 1` `        ``if` `((n + 1) % i == 0) {` `            ``cout << i << ``", "` `                 ``<< (n + 1) / i;` `            ``break``;` `        ``}`   `        ``// Check for condition 2` `        ``if` `((n + 2) % i == 0) {` `            ``cout << i << ``", "` `                 ``<< (n + 2) / i;` `            ``break``;` `        ``}` `    ``}` `}`   `// Driver Code` `int` `main()` `{` `    ``// Given Number` `    ``int` `N = 123;`   `    ``// Function Call` `    ``closestDivisors(N);` `}`

## Java

 `// Java program for the above approach` `import` `java.util.*;` `class` `GFG{` ` `  `// Function to print pair (a, b)` `// such that a*b=N+1 or N+2` `static` `void` `closestDivisors(``int` `n)` `{` `    ``// Loop to iterate over the` `    ``// desired possible values` `    ``for` `(``int` `i = (``int``)Math.sqrt(n + ``2``); i > ``0``; i--) ` `    ``{` ` `  `        ``// Check for condition 1` `        ``if` `((n + ``1``) % i == ``0``) ` `        ``{` `           ``System.out.print(i +  ``", "` `+` `                           ``(n + ``1``) / i);` `            ``break``;` `        ``}` ` `  `        ``// Check for condition 2` `        ``if` `((n + ``2``) % i == ``0``)` `        ``{` `            ``System.out.print(i + ``", "` `+ ` `                            ``(n + ``2``) / i);` `            ``break``;` `        ``}` `    ``}` `}` ` `  `// Driver Code` `public` `static` `void` `main(String[] args)` `{` `    ``// Given Number` `    ``int` `N = ``123``;` ` `  `    ``// Function Call` `    ``closestDivisors(N);` `}` `}`   `// This code is contributed by rock_cool`

## Python

 `# Python3 program for the above approach` `from` `math ``import` `sqrt, ceil, floor`   `# Function to prpair (a, b)` `# such that a*b=N+1 or N+2` `def` `closestDivisors(n):`   `    ``# Loop to iterate over the` `    ``# desired possible values` `    ``for` `i ``in` `range``(ceil(sqrt(n ``+` `2``)), ``-``1``, ``-``1``):`   `        ``# Check for condition 1` `        ``if` `((n ``+` `1``) ``%` `i ``=``=` `0``):` `            ``print``(i, ``","``, (n ``+` `1``) ``/``/` `i)` `            ``break`   `        ``# Check for condition 2` `        ``if` `((n ``+` `2``) ``%` `i ``=``=` `0``):` `            ``print``(i, ``","``, (n ``+` `2``) ``/``/` `i)` `            ``break` ` `  `# Driver Code` `if` `__name__ ``=``=` `'__main__'``:` `  `  `    ``# Given Number` `    ``N ``=` `123`   `    ``# Function Call` `    ``closestDivisors(N)`   `# This code is contributed by Mohit Kumar`

## C#

 `// C# program for the above approach` `using` `System;` `class` `GFG{` `  `  `// Function to print pair (a, b)` `// such that a*b=N+1 or N+2` `static` `void` `closestDivisors(``int` `n)` `{` `    ``// Loop to iterate over the` `    ``// desired possible values` `    ``for` `(``int` `i = (``int``)Math.Sqrt(n + 2); i > 0; i--) ` `    ``{` `  `  `        ``// Check for condition 1` `        ``if` `((n + 1) % i == 0) ` `        ``{` `           ``Console.Write(i +  ``", "` `+` `                           ``(n + 1) / i);` `            ``break``;` `        ``}` `  `  `        ``// Check for condition 2` `        ``if` `((n + 2) % i == 0)` `        ``{` `            ``Console.Write(i + ``", "` `+ ` `                         ``(n + 2) / i);` `            ``break``;` `        ``}` `    ``}` `}` `  `  `// Driver Code` `public` `static` `void` `Main(``string``[] args)` `{` `    ``// Given Number` `    ``int` `N = 123;` `  `  `    ``// Function Call` `    ``closestDivisors(N);` `}` `}` ` `  `// This code is contributed by Ritik Bansal`

Output:

```5, 25

```

Time Complexity: O(sqrt(N))
Auxiliary Space: O(1)

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