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Log_2aa=x    then, a=(2a)^x  ......(1)

Log_3a2a=y    then,2a=(3a)^y ......(2)

Log_4a 3a=z  then, 3a=(4a)^z ......(3)

So, 

a=(2a)^x  [from (1)]

Or, a=(3a)^xy    [from(2)]

Or, a=(4a)^xyz     [from(3)]

Multiplying both sides by 4a,

4a.a=4a.(4a)^xyz  

Or,(2a)² =(4a)^{xyz + 1} 

Or,(3a)^2y =(4a)^xyz+1 

Or,(4a)^2yz =(4a)^xyz+1 

Or, 2yz = xyz+1 .proved.

Hello Subash!

Here is the solution for the question you are asking for, I solved it in procedural way but if you are among the one who prefer OOP style then you can still ask it for me cause I have solved it from both methods but here I am just going to leave procedural one....

//author:Manish Acharya

import java.util.Scanner;

import java.util.*;

public class idgenerator {

public static void main(String[] args) {

String small_name="", long_name="", new_small_name="", new_long_name="";

char lr='a',...

the symbols used in the story are:

1. house and shops- it symbolizes Aksionov's family and material possessions
2. nightmare-it symbolizes a bad omen.
3. blood-stained knife- it indicates Aksionov's lack of control over his fate.
4. the prison- Aksionov's pain and subsequent mystical transformation are symbolized by the prison.
5. the book(the lives of the saints)- gives an impression of religiosity.