Use just logic

For students of class 6-8 (age 12 to 14)
sakibtanvir
Posts:188
Joined:Mon Jan 09, 2012 6:52 pm
Location:24.4333°N 90.7833°E
Use just logic

Unread post by sakibtanvir » Tue Feb 21, 2012 11:03 am

Prove that, there is no integer $n$ such that, for any prime $p$ , $2p+n$ will also be a prime.
(Without using any modular equation. :) )
(I proved it such that,a primary level student will easily understand my prof :mrgreen: )
An amount of certain opposition is a great help to a man.Kites rise against,not with,the wind.

User avatar
Phlembac Adib Hasan
Posts:1016
Joined:Tue Nov 22, 2011 7:49 pm
Location:127.0.0.1
Contact:

Re: Use just logic

Unread post by Phlembac Adib Hasan » Tue Feb 21, 2012 12:24 pm

Hint :
Do prime factorization of $n$.
Welcome to BdMO Online Forum. Check out Forum Guides & Rules

User avatar
nafistiham
Posts:829
Joined:Mon Oct 17, 2011 3:56 pm
Location:24.758613,90.400161
Contact:

Re: Use just logic

Unread post by nafistiham » Tue Feb 21, 2012 2:00 pm

if $n$ is prime, take $p=n$ if not, take $p$ as one of $n$'s prime factor.
\[\sum_{k=0}^{n-1}e^{\frac{2 \pi i k}{n}}=0\]
Using $L^AT_EX$ and following the rules of the forum are very easy but really important, too.Please co-operate.
Introduction:
Nafis Tiham
CSE Dept. SUST -HSC 14'
http://www.facebook.com/nafistiham
nafistiham@gmail

User avatar
Eesha
Posts:30
Joined:Tue Dec 07, 2010 8:43 pm
Location:23.755381,90.380636
Contact:

Re: Use just logic

Unread post by Eesha » Wed Dec 19, 2012 7:30 am

$n=1$ আর $p=3$ ধরি... তাহলে...
$2*3+1=7$
$7$তো প্রাইম তাইলে???
গণিত অলেম্পিয়াডে প্রাইজ পাওয়াটাই আসল না। প্রাইজ সবসময় পায়না এমন অনেকেও অনেক ভাল।

পরিচিতি
রাফিদ সাদমান ঈশা
জুনিয়র
ঢাকা

User avatar
Phlembac Adib Hasan
Posts:1016
Joined:Tue Nov 22, 2011 7:49 pm
Location:127.0.0.1
Contact:

Re: Use just logic

Unread post by Phlembac Adib Hasan » Wed Dec 19, 2012 9:03 pm

Eesha wrote:$n=1$ আর $p=3$ ধরি... তাহলে...
$2*3+1=7$
$7$তো প্রাইম তাইলে???
sakibtanvir wrote:Prove that, there is no integer $n$ such that, for any prime $p$ , $2p+n$ will also be a prime.
(Without using any modular equation. :) )
(I proved it such that,a primary level student will easily understand my prof :mrgreen: )
here 'any' means 'every'. $p=7$ contradicts with $n=1$.
Welcome to BdMO Online Forum. Check out Forum Guides & Rules

User avatar
Thanic Nur Samin
Posts:176
Joined:Sun Dec 01, 2013 11:02 am

Re: Use just logic

Unread post by Thanic Nur Samin » Tue Jan 28, 2014 4:50 pm

nafistiham wrote:if $n$ is prime, take $p=n$ if not, take $p$ as one of $n$'s prime factor.
what if $n=1$?
Hammer with tact.

Because destroying everything mindlessly isn't cool enough.

Post Reply