Competition problem — Algebra — Maths Olympiad Prep

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Algebra Difficulty 4.9 AIME Find the answer

What is the remainder when $2^{2001}$ is divided by $2^{7}-1$ ?

Your answer

A number or a short expression. Spacing and $ signs are ignored.

Solution

$2^{2001(\bmod 7)}=2^{6}=64$ .

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