2026-04-26

Problem — 2026-04-26

Easy

Easynumber_theory

What is the remainder when $2^{100}$ is divided by $7$ ?

Enter an integer (0 to 6)

Show solution

By Fermat's little theorem,

2^6 \equiv 1 \pmod{7}

. Since

100 = 6 \cdot 16 + 4

, we have

2^{100} = (2^6)^{16} \cdot 2^4 \equiv 1^{16} \cdot 16 \equiv 16 \equiv 2 \pmod{7}