# Find x and y satisfying ax + by = n

• Difficulty Level : Easy
• Last Updated : 18 Jul, 2022

Given a, b and n. Find x and y that satisfies ax + by = n. Print any of the x and y satisfying the equation
Examples :

```Input : n=7 a=2 b=3
Output : x=2, y=1
Explanation: here x and y satisfies the equation

Input : 4 2 7
Output : No solution```

We can check if any solutions exists or not using Linear Diophantine Equations, but here we need to find out the solutions for this equation, so we can simply iterate for all possible values from 0 to n as it cannot exceed n for this given equation. So solving this equation with pen and paper gives y=(n-ax)/b and similarly we get the other number to be x=(n-by)/a.If none of the values satisfies the equation, at the end we print “no solution”

## C++

 `// CPP program to find solution of ax + by = n` `#include ` `using` `namespace` `std;`   `// function to find the solution` `void` `solution(``int` `a, ``int` `b, ``int` `n)` `{` `    ``// traverse for all possible values` `    ``for` `(``int` `i = 0; i * a <= n; i++) {`   `        ``// check if it is satisfying the equation` `        ``if` `((n - (i * a)) % b == 0) {` `            ``cout << ``"x = "` `<< i << ``", y = "` `                 ``<< (n - (i * a)) / b;` `            ``return``;` `        ``}` `    ``}`   `    ``cout << ``"No solution"``;` `}`   `// driver program to test the above function` `int` `main()` `{` `    ``int` `a = 2, b = 3, n = 7;` `    ``solution(a, b, n);` `    ``return` `0;` `}`

## Java

 `// Java program to find solution` `// of ax + by = n` `import` `java.io.*;`   `class` `GfG {` `        `  `    ``// function to find the solution` `    ``static` `void` `solution(``int` `a, ``int` `b, ``int` `n)` `    ``{` `        ``// traverse for all possible values` `        ``for` `(``int` `i = ``0``; i * a <= n; i++)` `        ``{` `    `  `            ``// check if it is satisfying the equation` `            ``if` `((n - (i * a)) % b == ``0``)` `            ``{` `                ``System.out.println(``"x = "` `+ i + ` `                                   ``", y = "` `+ ` `                                   ``(n - (i * a)) / b);` `                `  `                ``return` `;` `            ``}` `        ``}` `    `  `        ``System.out.println(``"No solution"``);` `    ``}` `    `  `    `  `    ``public` `static` `void` `main (String[] args) ` `    ``{` `        ``int` `a = ``2``, b = ``3``, n = ``7``;` `        ``solution(a, b, n);` `    `  `    ``}` `}`   `// This code is contributed by Gitanjali.`

## Python3

 `# Python3 code to find solution of` `# ax + by = n`   `# function to find the solution` `def` `solution (a, b, n):`   `    ``# traverse for all possible values` `    ``i ``=` `0` `    ``while` `i ``*` `a <``=` `n:` `        `  `        ``# check if it is satisfying` `        ``# the equation` `        ``if` `(n ``-` `(i ``*` `a)) ``%` `b ``=``=` `0``:` `            ``print``(``"x = "``,i ,``", y = "``,` `               ``int``((n ``-` `(i ``*` `a)) ``/` `b))` `            ``return` `0` `        ``i ``=` `i ``+` `1` `    `  `    ``print``(``"No solution"``)`   `# driver program to test the above function` `a ``=` `2` `b ``=` `3` `n ``=` `7` `solution(a, b, n)`   `# This code is contributed by "Sharad_Bhardwaj".`

## C#

 `// C# program to find solution` `// of ax + by = n` `using` `System;`   `class` `GfG {` `        `  `    ``// function to find the solution` `    ``static` `void` `solution(``int` `a, ``int` `b, ``int` `n)` `    ``{` `        `  `        ``// traverse for all possible values` `        ``for` `(``int` `i = 0; i * a <= n; i++)` `        ``{` `    `  `            ``// check if it is satisfying the` `            ``// equation` `            ``if` `((n - (i * a)) % b == 0)` `            ``{` `                ``Console.Write(``"x = "` `+ i + ` `                                ``", y = "` `+ ` `                        ``(n - (i * a)) / b);` `                `  `                ``return` `;` `            ``}` `        ``}` `    `  `        ``Console.Write(``"No solution"``);` `    ``}` `    `  `    ``// Driver code` `    ``public` `static` `void` `Main () ` `    ``{` `        ``int` `a = 2, b = 3, n = 7;` `        ``solution(a, b, n);` `    `  `    ``}` `}`   `// This code is contributed by Vt_m.`

## PHP

 ``

## Javascript

 ``

Output

`x = 2, y = 1`

Time Complexity: O(n/a), as we are using a loop to traverse n/a times.
Auxiliary Space: O(1), since no extra space has been taken.

My Personal Notes arrow_drop_up
Recommended Articles
Page :