Determine n

For discussing Olympiad Level Number Theory problems
Katy729
Posts:47
Joined:Sat May 06, 2017 2:30 am
Determine n

Unread post by Katy729 » Sun May 21, 2017 2:44 am

Determine if there are integers $n$ so that $n^2-4$ has exactly $10$ divisors (positive).

User avatar
asif e elahi
Posts:185
Joined:Mon Aug 05, 2013 12:36 pm
Location:Sylhet,Bangladesh

Re: Determine n

Unread post by asif e elahi » Fri Jun 02, 2017 8:49 am

Sketch:
Suppose $n$ is such an integer. Prove that $n^2-4=pq^4$ for some prime $p,q$. Deduce that $q=2$.......

Post Reply