alleryThe remainder when $2^{100}$ is divided by 7 is
A4
B1
C2
D5
Answer & Solution
Correct answer: C. 2
Powers of 2 mod 7 cycle: $2,4,1$ with period 3. $100 \equiv 1 \pmod 3$, so $2^{100} \equiv 2^1 = 2 \pmod 7$.
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