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 )
Use just logic
-
- Posts:188
- Joined:Mon Jan 09, 2012 6:52 pm
- Location:24.4333°N 90.7833°E
An amount of certain opposition is a great help to a man.Kites rise against,not with,the wind.
- Phlembac Adib Hasan
- Posts:1016
- Joined:Tue Nov 22, 2011 7:49 pm
- Location:127.0.0.1
- Contact:
- nafistiham
- Posts:829
- Joined:Mon Oct 17, 2011 3:56 pm
- Location:24.758613,90.400161
- Contact:
Re: Use just logic
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.
Using $L^AT_EX$ and following the rules of the forum are very easy but really important, too.Please co-operate.
Re: Use just logic
$n=1$ আর $p=3$ ধরি... তাহলে...
$2*3+1=7$
$7$তো প্রাইম তাইলে???
$2*3+1=7$
$7$তো প্রাইম তাইলে???
গণিত অলেম্পিয়াডে প্রাইজ পাওয়াটাই আসল না। প্রাইজ সবসময় পায়না এমন অনেকেও অনেক ভাল।
পরিচিতি
পরিচিতি
- Phlembac Adib Hasan
- Posts:1016
- Joined:Tue Nov 22, 2011 7:49 pm
- Location:127.0.0.1
- Contact:
Re: Use just logic
Eesha wrote:$n=1$ আর $p=3$ ধরি... তাহলে...
$2*3+1=7$
$7$তো প্রাইম তাইলে???
here 'any' means 'every'. $p=7$ contradicts with $n=1$.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 )
Welcome to BdMO Online Forum. Check out Forum Guides & Rules
- Thanic Nur Samin
- Posts:176
- Joined:Sun Dec 01, 2013 11:02 am
Re: Use just logic
what if $n=1$?nafistiham wrote:if $n$ is prime, take $p=n$ if not, take $p$ as one of $n$'s prime factor.
Hammer with tact.
Because destroying everything mindlessly isn't cool enough.
Because destroying everything mindlessly isn't cool enough.