Find the remainder when (100+3)^105 is divided by 3.
Note
First, we simplify the base: (100+3) = 103. Now we reduce the base to 3 modulo: 103 ≡ 1 (mod 3). Since any positive power of 1 is 1, 103^105 ≡ 1^105 ≡ 1 (mod 3). So the remainder is 1.
Find the remainder when (100+3)^105 is divided by 3.
First, we simplify the base: (100+3) = 103. Now we reduce the base to 3 modulo: 103 ≡ 1 (mod 3). Since any positive power of 1 is 1, 103^105 ≡ 1^105 ≡ 1 (mod 3). So the remainder is 1.