BOMC-2012 Test Day 1 Problem 3
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 \[n\in N\]
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- Phlembac Adib Hasan
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Re: BOMC-2012 Test Day 1 Problem 3
There is no such a sequence.
Hint :
Hint :
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- Nadim Ul Abrar
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Re: BOMC-2012 Test Day 1 Problem 3
Yess ..
$mod 3$ , and $modp_1$ kills the problem ...
$mod 3$ , and $modp_1$ kills the problem ...
$\frac{1}{0}$
Re: BOMC-2012 Test Day 1 Problem 3
I myself used $\bmod 6$ and $\bmod p_2$, as whatever $p_1$ is, $p_2$ must be odd.
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Re: BOMC-2012 Test Day 1 Problem 3
I can't solve.
What's the process
What's the process
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Re: BOMC-2012 Test Day 1 Problem 3
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
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- nafistiham
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Re: BOMC-2012 Test Day 1 Problem 3
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 $3$
\[\sum_{k=0}^{n-1}e^{\frac{2 \pi i k}{n}}=0\]
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