题解 | #进制均值#

import java.util.Scanner;

/**
 * JD8 进制均值
 * @author d3y1
 */
public class Main {
    public static void main(String[] args){
        Scanner in = new Scanner(System.in);

        while(in.hasNext()){
            // solution1(in);
            solution2(in);
        }
    }

    /**
     * 模拟法: 最大公约数
     * @param in
     */
    private static void solution1(Scanner in){
        int A = in.nextInt();

        int sum = 0;
        int div,mod;
        for(int i=2; i<A; i++){
            div = A;
            while(div > 0){
                mod = div%i;
                div = div/i;
                sum += mod;
            }
        }

        int dividend = sum;
        int divisor = A-2;
        int gcd = gcd(dividend, divisor);

        System.out.println(dividend/gcd+"/"+divisor/gcd);
    }

    /**
     * 最大公约数
     * @param a
     * @param b
     * @return
     */
    private static int gcd(int a, int b){
        return b>0 ? gcd(b, a%b) : a;
    }

    /**
     * 模拟法
     * @param in
     */
    private static void solution2(Scanner in){
        int A = in.nextInt();

        int sum = 0;
        int div,mod;
        for(int i=2; i<A; i++){
            div = A;
            while(div > 0){
                mod = div%i;
                div = div/i;
                sum += mod;
            }
        }

        int dividend = sum;
        int divisor = A-2;
        for(int i=2; i<=divisor; i++){
            while(dividend%i==0 && divisor%i==0){
                dividend /= i;
                divisor /= i;
            }
        }

        System.out.println(dividend+"/"+divisor);
    }
}