Pairing up consecutive numbers may give a prime..(Self-made)

For discussing Olympiad Level Number Theory problems
Facebook Twitter

Pairing up consecutive numbers may give a prime..(Self-made)

Post Number:#1  Unread postby Fm Jakaria » Sat Jul 08, 2017 10:45 pm

Is it true that for each even positive integer $n$, the integers $1$ through $n$ can be paired with each other into $\frac{n}{2}$ pairs - so that the product of each pairs, when summed up - gives a prime number?

For example, for $n = 8$, we can pair up $1,7$; $2,8$; $3,6$; $4,5$. Then $1*7+ 2*8+ 3*6+ 4*5$ equals $61$, a prime.....

If this isn't true, find the least counterexample $n$.
Fm Jakaria
 
Posts: 77
Joined: Thu Feb 28, 2013 11:49 pm

Share with your friends: Facebook Twitter

  • Similar topics
    Replies
    Views
    Author

Return to Number Theory

Who is online

Users browsing this forum: No registered users and 1 guest

cron