Automorphic Number in Python

A number is said to be an automorphic number if the last digits of the square of this number give the same number.

The following are the examples of automorphic numbers-

1. Input: 25

Output - Yes, it is an automorphic number.

Reason - The square of 25 gives 625, since the last digits are 25 it is an automorphic number.

2. Input: 14

Output - No, it is not an automorphic number.

Reason - The square of 14 gives 196, since the last digits are 96 it is not an automorphic number.

3. Input: 76

Output - Yes, it is an automorphic number.

Reason - The square of 76 gives 6776, since the last digits are 76 it is an automorphic number.

Since the concept is clear to us now, let us see how we can build the logic to check whether a number is automorphic or not.

We know that the modulus operator can be used to perform functions on the digits of a number.

The following illustrates how it can be done in Python.

Example -

num = int(input("Enter a number you want to check: \n"))

#calculating the number of digits
num_of_digits = len(str(num))

#computing the square of a number
square = num**2

#obtaining the last digits 
last_digits = square%pow(10,num_of_digits)

#comparing the digits of number with input
if last_digits == num:
  print("Yes, {} is an automorphic number".format(num))
else:
  print("No, {} is not an automorphic number".format(num))

Output

Enter a number you want to check: 
76
Yes, 76 is an automorphic number

So, let's have a glance at the step-by-step approach of the same-

The first step will be to take the number from the user and calculate its square.
We can calculate the number of digits by using the len function.
The next thing is to calculate the square of a number.
Now, we will make use of the power function and modulus operator to obtain the last digits.
Finally, we will compare the last digit with the input number.
On executing the program, the desired output will be displayed.

Let us see what happens when we pass the numbers that we discussed in the example.

Since 25 is an automorphic number, it displays the required message.

Output - 2

Enter a number you want to check: 
25
Yes, 25 is an automorphic number

Since 14 is not an automorphic number, it displays the required message.

Output - 3

Enter a number you want to check: 
14
No, 14 is not an automorphic number

Using While loop

The next approach to do the same is as follows-

Example -

print("Enter the number you want to check:")
num=int(input())
square=num*num  
flag=0 
while(num>0): 
    if(num%10!=square%10):
        print("No, it is not an automorphic number.")
        flag=1
        break                     
     
    num=num//10                      
    square=square//10 

if(flag==0):
    print("Yes, it is an automorphic number.")

Output

Enter the number you want to check:

25
Yes, it is an automorphic number.

Let us understand the steps we have followed in this program-

The first step remains the same, that is, to take the number from the user and calculate its square.
We have declared a while loop which will execute till the number becomes zero.
Now we will compare whether the units digit of a number is equal to the unit place of the number obtained after computing the square.
If the above condition is satisfied, then we will go for the floor division of the number and the squared number.
On executing the program, it displays whether the number is an automorphic number or not.

So, in this article, we learned what an automorphic number is and how we can check whether a given number is automorphic or not using Python.

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