Find the remainder when \(25^{18}\) is divided by 9.

A. 1
B. 2
C. 3
D. 5
E. 6

METHOD I : Euler no of 9 = 9(1-1/3) = 6
rem [(25^18) /9]
= rem [(25^0)/9] [ 18 is divisible by 6 ]
= rem [1/9]
= 1

METHOD II : rem [(25^18 )/9]
=rem [ (-2)^18 /9] [ rem (25/9) = -2 ]
=rem [ (+2)^18 /9]
=rem [ (2^6) * ( 2^6 )* (2^6 )/9]
=rem [ 64*64*64 /9]
=rem [1*1*1 /9]
=1

METHOD III : rem [(25^18 )/9]
= rem [ (27-2)^18/9] [ using binomial theorem ]
=rem [ (-2)^18 /9] [ considering only last term since rest all terms will be divisible by 9 ]
=rem [ (+2)^18 /9]
=rem [ (2^6) * ( 2^6 )* (2^6 )/9]
=rem [ 64*64*64 /9]
=rem [1*1*1 /9]
=1

correct answer is A