pku acm 1183

 

推导过程：

1/a = (1/b + 1/c)/ (1 - 1/(b*c)) => bc-1 = a(b+c)

 assume b=a+m and c=a+n (b and c is always bigger than a)

 (a+m)(a+n)-1=a(a+m+a+n) => a*a+a*n+a*m+m*n-1=2*a*a+m*a+n*a => m*n=a*a+1 and then

 for(m=a;m>=1;m--)

 if((a*a+1)%m==0) break;

 n=(a*a+1)/m

import java.util.Scanner; public class Main{ public static void main(String[] args)throws Exception{ Scanner cin=new Scanner(System.in); long a=cin.nextInt(); long m=0,n=0; for(m=a;m>=1;m--){ if((a*a+1)%m==0)break; } n=(a*a+1)/m; System.out.println(2*a+m+n); } }