Find all integers $n>1$ such that $n^2|2^n+1$.

Question

$3$ is clearly an example, but I can't seem to find any other. How do I prove (or disprove) that $3$ is the unique solution?

Let $p$ be a prime dividing $n$, and use the Little Fermat Theorem. — Gerry Myerson, Oct 15 '17 at 06:39

score 0 · Answer 1 · answered Oct 15 '17 at 06:15

0

Unanswered queue is already quite long!!!

[Here is the answer] ( [PDF] an 소 1 - Yufei Zhao yufeizhao.com › exponent_lifting_sol). Go to answer 6.

It would be good if you learn LTE technique from a good resource if you are doing Olympiad problems. Maybe from here

answered Oct 15 '17 at 06:15

Vidyanshu Mishra

Is that really a link? How does it work? – Gerry Myerson Oct 15 '17 at 06:38
Copy [PDF] ...._lifting_sol and paste wherever you want @GerryMyerson – Vidyanshu Mishra Oct 15 '17 at 06:53
I think http://yufeizhao.com/olympiad/exponent_lifting_sol.pdf would be a much better way to give the link. – Gerry Myerson Oct 15 '17 at 07:45

1 Answers1