Library / UKMT Senior Mathematical Challenge /190 of 212

UKMT Senior Mathematical Challenge, 2023

Number theory Difficulty 3.0 AMC 10/12 Find the answer United Kingdom

How many of the numbers $6, 7, 8, 9, 10$ are factors of the sum $2^{2024} + 2^{2023} + 2^{2022}$ ?

(A) $1$ (B) $2$ (C) $3$ (D) $4$ (E) $5$

We don't reproduce this publisher's solutions. Their own solution is here — work the problem first.

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: UK Mathematics Trust, licensed © UK Mathematics Trust; past papers published free at ukmt.org.uk. Statement reproduced verbatim; metadata (topic, difficulty) added by this project. Solutions are the publisher's, linked not copied.