What is $2^{20} \bmod 7$?

Explanation

1. 01

   $2^{3} = 8 \equiv 1 \pmod{7}$, so the powers of 2 repeat every 3.

2. 02

   $2^{20} = (2^{3})^{6} \times 2^{2} \equiv 1 \times 4 = 4 \pmod{7}$.