Question

Find remainder in 4^2022/15

Answer 1

1

Answer 2

We need to compute $4^{2022} \mod 15$.

Step 1:
Note that:

$$4^2 = 16 \equiv 1 \pmod{15}$$

Step 2:
Since $4^2 \equiv 1$, we can write:

$$4^{2022} = (4^2)^{1011} \equiv 1^{1011} \equiv 1 \pmod{15}$$

The remainder when $4^{2022}$ is divided by 15 is 1.

Since $4^2 \equiv 1 \mod 15$, write $4^{2022}=(4^2)^{1011}$ so that $4^{2022}\equiv 1^{1011}\equiv 1 \mod 15$.