Enter a number to check if it's automorphic, or generate all automorphic numbers in a range.
An automorphic number is a number whose powers end in the same digits as the number itself. In other words, if a number \( n \), when raised to any power, retains its own digits as the ending digits of the result, then \( n \) is an automorphic number. Automorphic numbers are categorized by the degree of the power:
For example: A number might not be a 2nd-degree automorphic number but could still qualify for higher degrees. Some numbers, like 5, are automorphic across multiple degrees (e.g., 2nd, 3rd, 4th, etc.).
Solution:
Square Calculation: \( 5^2 = 25 \)
Ending Check: The last digit of 25 is 5, which matches the original number.
Result: 5 is an automorphic number.
Solution:
Square Calculation: \( 4^2 = 16 \)
Ending Check: The last digit of 16 is 6, which does not match 4.
Cube Calculation: \( 4^3 = 64 \)
Ending Check: The last digit of 64 is 4, which matches the original number.
Result: 4 is a 3rd-degree automorphic number.
Solution:
Square Calculation: \( 25^2 = 625 \)
Ending Check: The last two digits of 625 are 25, matching the original number.
Result: 25 is an automorphic number.
Solution:
Square Calculation: \( 12^2 = 144 \)
Ending Check: The last two digits of 144 are 44, which do not match 12.
Result: 12 is not a 2nd-degree automorphic number.