for prime (a,b).....

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photon
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for prime (a,b).....

Unread post by photon » Wed Jan 11, 2012 10:26 pm

find prime (a,b) sothat $a^b+b^a$ is also a prime.
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afif mansib ch
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Re: for prime (a,b).....

Unread post by afif mansib ch » Wed Jan 11, 2012 11:12 pm

(1,2),(2,3)
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Re: for prime (a,b).....

Unread post by nafistiham » Thu Jan 12, 2012 12:48 am

afif mansib ch wrote:(1,2),(2,3)
As far as I know $1$ is not prime. :D
\[\sum_{k=0}^{n-1}e^{\frac{2 \pi i k}{n}}=0\]
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afif mansib ch
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Re: for prime (a,b).....

Unread post by afif mansib ch » Thu Jan 12, 2012 12:42 pm

ok then (2,3)only!!! :mrgreen:
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Re: for prime (a,b).....

Unread post by photon » Thu Jan 12, 2012 9:36 pm

afif mansib ch wrote:ok then (2,3)only!!! :mrgreen:
why don't you post your proof ? giving just the answers reminds me about talking answers in exam hall. :D
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afif mansib ch
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Re: for prime (a,b).....

Unread post by afif mansib ch » Fri Jan 13, 2012 12:57 am

1st i tried with trivial magnitudes like 1,2,3.
then for any prime a and b>3
\[a^b,b^a\equiv 1(mod2)\]
so\[a^b+b^a=p\equiv 0(mod2)\]
which can't be prime.
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Masum
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Re: for prime (a,b).....

Unread post by Masum » Fri Jan 13, 2012 2:28 pm

afif mansib ch wrote:(1,2),(2,3)
$1$ is neither prime nor composite.
One one thing is neutral in the universe, that is $0$.
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Tahmid Hasan
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Re: for prime (a,b).....

Unread post by Tahmid Hasan » Fri Jan 13, 2012 2:31 pm

afif mansib ch wrote:1st i tried with trivial magnitudes like 1,2,3.
then for any prime a and b>3
\[a^b,b^a\equiv 1(mod2)\]
so\[a^b+b^a=p\equiv 0(mod2)\]
which can't be prime.
what about considering the case when one is $2$ :?:
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Re: for prime (a,b).....

Unread post by sourav das » Fri Jan 13, 2012 3:07 pm

Just take mod (3)
You spin my head right round right round,
When you go down, when you go down down......(-$from$ "$THE$ $UGLY$ $TRUTH$" )
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afif mansib ch
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Re: for prime (a,b).....

Unread post by afif mansib ch » Fri Jan 13, 2012 8:29 pm

as sourav via said i proved it for 2 also.(but only 15 days left for s.s.c.so i enter the forum hiding.it's hard to post full sol bcause 'f time)lol. :mrgreen:
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