Find the remainder when 2^100 is divided by 3.
Note
Powers of 2 modulo 3 cycle: 2^1≡2, 2^2≡1, then repeat with period 2; since 100 is even, 2^100≡1 (mod 3), so remainder 1.
Find the remainder when 2^100 is divided by 3.
Powers of 2 modulo 3 cycle: 2^1≡2, 2^2≡1, then repeat with period 2; since 100 is even, 2^100≡1 (mod 3), so remainder 1.