Find the remainder when 40^{13} is divided by 81.

Answer 1

To find the remainder when 40^{13} is divided by 81, we can use Euler's theorem.

Since 81 = 3^4, we need to find the remainder of 40^{13} when divided by 3^4.

First, we compute the remainder when 40 is divided by 3:
40 ÷ 3 = 13 remainder 1

Next, we calculate the remainder when 40^{13} is divided by 3^4:
Since 40 mod 3 = 1, we have:
1^{13} mod 3^4 = 1 mod 81 = 1

Therefore, the remainder when 40^{13} is divided by 81 is 1.