Prove that kk is periodic mod 3 and find its periodSolutionW

Prove that {k^k} is periodic (mod 3) and find its period.

WHAT IS MEANT BY {KK} ...

I HAVE NOT COME ACROSS SUCH A NOMEN CLATURE SO FAR .

I SEARCHED THE NET ,BUT IT GIVES SOME FUNCTION HALLS BY NAME KK ..SO WHAT IS IT ?

IF YOU ELABORATE WHAT IT IS ..SAY IT IS FUNCTION OR SET R WHATEVER , THEN WE CAN GIVE YOU THE SOLUTION ON HOW TO PROVE IT IS PERIODIC.

IF IT IS ANY FUNCTION SAY ...SIN[3T] ......TO FIND ITS PERIOD , WE ASSUME THE PERIOD ID P ..SO WE SHALL HAVE ..

SIN[3T]=SIN[3(T+P)] ...BUT WE KNOW THAT SIN[3T]=SIN[3T+2*PI] ..SO WE GET ...

SIN[3(T+P)] = SIN(3T+2*PI]

3T +3P = 3T + 2*PI

P = 2*PI/3 ...SO SIN [3T] IS PERIODIC WITH PERIOD OF 2*PI/3 ..

TC..