Competition problem — Number theory

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Number theory Difficulty 4.1 AIME Find the answer United States

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

Your answer

A number or a short expression. Fractions can be typed as 3/2, and spacing doesn't matter.

Solution

Solution:
$2^{2001 \bmod 7} = 2^{6} = 64$ .

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Source: MathNet, licensed CC-BY-4.0. Statement reproduced verbatim; metadata (topic, difficulty) added by this project.