Question

Determine n between 0 and 8 such that 1111^2222  = n mod 9.

Answer 1

1111 = 123 x 9 + 4 = 4 mod 9
1111^2 = 4^2 mod 9 = 7 mod 9
1111^3 = 4^3 mod 9 = 1 mod 9
1111^4 = 4^4 mod 9 = 4 mod 9

2222 = 740 x 3 +2 = 2 mod 3
1111^2222 = 7 mod 9

n = 7