BOMC-2012 Test Day 1 Problem 3
Posted: Wed Apr 11, 2012 11:07 pm
Determine if there exists an infinite sequence of prime numbers \[p_1, p_2,..., p_n,... \] such that \[|p_{n+1}- 2p_n|=1\]for each \[n\in N\]
Hint :
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BOMC-2012 Test Day 1 Problem 3
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Re: BOMC-2012 Test Day 1 Problem 3
Posted: Thu Apr 12, 2012 11:52 am
There is no such a sequence.
Hint :
Hint :
Re: BOMC-2012 Test Day 1 Problem 3
Posted: Thu Apr 12, 2012 1:09 pm
Yess ..
$mod 3$ , and $modp_1$ kills the problem ...
$mod 3$ , and $modp_1$ kills the problem ...
Re: BOMC-2012 Test Day 1 Problem 3
Posted: Thu Apr 12, 2012 7:13 pm
I myself used $\bmod 6$ and $\bmod p_2$, as whatever $p_1$ is, $p_2$ must be odd.
Re: BOMC-2012 Test Day 1 Problem 3
Posted: Thu Apr 12, 2012 10:31 pm
I can't solve. 
What's the process
What's the process
Re: BOMC-2012 Test Day 1 Problem 3
Posted: Fri Apr 13, 2012 12:20 am
If you take $\pmod 6$, you can show that if $p_2$ is of the form $6k+1$ or $6k-1$, then all $p_i$ must be of the form $6k+1$ or $6k-1$ respectively. Then try induction to get the general form of $p_x$.sm.joty wrote:I can't solve.
What's the process
Re: BOMC-2012 Test Day 1 Problem 3
Posted: Fri Apr 13, 2012 6:06 pm
I used contradiction.
Firstly, made a system that must include such a sequence (if it existed!)
using $\bmod 3$ proved that every sequence in that system includes infinitely many multiples of $3$
Firstly, made a system that must include such a sequence (if it existed!)
using $\bmod 3$ proved that every sequence in that system includes infinitely many multiples of $3$