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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
Updated on: 01-Feb-2022
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