Automorphic number using Python

January 13, 2021

Automorphic Number:

In mathematics, an automorphic number (sometimes referred to as a circular number) is a natural number in a given number base b whose square end in the same digits as the number itself.

Example:

  •  n=25,
    • 25*25=625
    • Output: Automorphic
  • n=70,
    • 70*70=4900
    • Output: Not Automorphic
Finding automorphic number using python

Implementation:

  • Evaluate the square of the given number (sq).
  • Loop until the given number becomes zero.
  • Check if  digit on the unit place of the given number is equal to digit on the unit place of the square number.
  • If the above condition holds true ,  reduce the number as n=n/10 and sq=sq/10.

  • Else return false.

Python Code:

1st Approach

#enter the number to check
print(‘Enter the number:’)
n=int(input())
sq=n*n #square of the given number 
co=0 #condition variable
while(n>0): #loop until n becomes 0
    if(n%10!=sq%10):
        print(‘Not Automorphic’)
        co=1
        break                    # come out of the loop if the above condition holds true 
    #reduce n and square 
    n=n//10                      
    sq=sq//10 

if(co==0):
    print(‘Automorphic’)

2nd Approach

 

n=int(input(“Enter any number”))
x=n**2
a=str(n)
b=str(x)
y=len(a)
z=len(b)
if(z-b.find(a)==y):
    print(“Automorphic”)
else:
    print(“Not automorphic number”)
Output:

Enter the number:

376

Automorphic