Automorphic Number

Number Theory Level 2

Which one of the following is an automorphic number?

Clarafications : An automorphic number is the number which is contained in the last digit(s) of its square .

Bonus: Is 0 an automorphic number?

76 25 Both 25 and 76 10 Both 25 and 10 Both 10 and 76

1 solution

Ram Mohith
Mar 22, 2018

The given three numbers are 10 , 25 , 76 .

${\color{#3D99F6}1}{\color{#E81990}0}^2 = 1\color{#E81990}00$

${\color{#3D99F6}2}{\color{#E81990}5}^2 = 6{\color{#3D99F6}2}{\color{#E81990}5}$

${\color{#3D99F6}7}{\color{#E81990}6}^2 = 57{\color{#3D99F6}7}{\color{#E81990}6}$

Therefore out of the given numbers only ${\color{#3D99F6}2}{\color{#E81990}5}~and~{\color{#3D99F6}7}{\color{#E81990}6}$ are Automorphic Numbers .

Bonus Question :

${\color{#3D99F6}0^2} = {\color{#3D99F6}00}$

Hence, $0$ is also an Automorphic number.

Is 0 an Automorphic Number?

Vaibhav Priyadarshi - 3 years, 1 month ago

Definitely yes

Ram Mohith - 3 years, 1 month ago