What is the remainder if $2^{192}$ is divided by 6?
What is the remainder if $2^{192}$ is divided by 6?
0
1
2
4
Solution
Powers of 2 mod 6: $2^1 = 2$, $2^2 = 4$, $2^3 \equiv 2$, $2^4 \equiv 4$. For even exponents the remainder is 4 and for odd exponents it is 2. Since 192 is even, $2^{192} \bmod 6 = 4$.