HMMT February

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. Fractions can be typed as 3/2, and spacing doesn't matter.

Solution

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

Want a route through all this instead of an archive? The track puts 2,604 problems in a working order, from Junior Challenge level to the IMO shortlist.

Source: Omni-MATH, licensed Apache-2.0. Statement reproduced verbatim; metadata (topic, difficulty) added by this project.