Find The Last 3 digits of the number $2003^{2002^{2001}}$
BY number theory or otherwise,
Also i would like to ask is there a property observed in the numbers of the form $k^n$, where for some $k, n$ is varied then the digits of $k^n$ are periodic,
for example,
$2^n$, its last digit is periodic with period 4, its second last digit is periodic $4\cdot 5 = 20$ its third last digit is periodic with periodic with period $20\cdot 5 =100$
I have observed this property with other numbers as well, though period might vary,for different values of $k$.