What is automorphic number? Please can u explain in detail?

Answer 1

Examples :
1 digit autom. n. = 5 => 5*5 = 25
^ ^

2 digit autom. n. = 76 => 76*76 = 5776
^ ^ ^ ^

3 digit autom. n. = 376 =>
376*376 = 141376
^ ^ ^ ^ ^ ^

Answer 2

"Its basically the number, whos square ends with the same digit(s) as the number itself."

That means if we take the number 5:

5*5 = 25 so 5 is a automorphic number.
^ ^

if we take 4:

4*4 = 16 it isnt a autom. number
^ ^

But for what do we use this?

So its just a number property, which we can use as any characteristic for example in a RAND algorithm.
Heres a simple searcher for those numbers of 1 - 999 (C++):

#include <iostream>
using namespace std;

void main()
{
  int Square,AuNum,mod;

  cout << "Automorphic Number from 1 to 999:\n “ ;

//less 10
  for(AuNum = 2; AuNum < 10; AuNum++)
  {
      Square = AuNum * AuNum;
      mod = Square%10;

if(AuNum == mod)
  cout << "Number: " << AuNum << " Square: " << Square << endl;
  }

//greater 10
for(AuNum = 10; AuNum < 100; i++)
  {
      Square = AuNum*AuNum;
      mod = Square%100;
      if(AuNum == mod)
  cout << "Number: " << AuNum << " Square: " << Square << endl; 
}
}

Like as any other property of number has automorphic number also a mathematical description of it. It exist some formula to find those numbers, but depends on the amount of the digits.
A formula for a 2 digit automorfic Number:
(src = Wikipedia)

n' = (3*n^2 - 2*n^3) mod 10^2k

n' : automorphic Number
n : input
k: digits

...

The special thing of it is, that you have pretty far pretty high numbers. So it helps for big RAND algs as I said. It would be amaizing to see some patterns of it. ;)

I hope I could help

Answer 3

can u give example with 2 or 3 digit number please.... ND tq

Answer 4

tq sooo much 😀😀