Find x, y, z that satisfy 2/n = 1/x + 1/y + 1/z in C++

In this problem, we are given integer values n. Our task is to find x, y, z that satisfy 2/nx + 1/y + 1/z.

Let's take an example to understand the problem,

Input : n = 4
Output : 4, 5, 20

Solution Approach

A simple solution to the problem is by finding the solution using the value of n.

If n = 1, no solution for the equation.

If n > 1, the solution to the equation is x = n, y = n+1, z = n(n+1).

The solution is $2/n\:=\:1/n\:+1\:(n+1)\:+\:1/(n^*(n\:+\:1))$

Example

Program to illustrate the working of our solution

#include <iostream>
using namespace std;
void findSolution(int a, int b, int n){
   for (int i = 0; i * a <= n; i++) {
      if ((n - (i * a)) % b == 0) {
         cout<<i<<" and "<<(n - (i * a)) / b;
         return;
      }
   }
   cout<<"No solution";
}
int main(){
   int a = 2, b = 3, n = 7;
   cout<<"The value of x and y for the equation 'ax + by = n' is ";
   findSolution(a, b, n);
   return 0;
}

Output

The value of x and y for the equation 'ax + by = n' is 2 and 1

sudhir sharma

Updated on 01-Feb-2022 08:40:01

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