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Ask iit jee aieee pet cbse icse state board experts Expert Question: NUMBER THEORy
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[Post New]13 Jun 2007 22:57:49 IST
    Subject: NUMBER THEORy
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p.t there is only one pair of twin primes s.t. (p+q)/2 is a square no.PLEASE ANSWER QUICKLY AND I WILL RATE YOU CERTAINLY.
    
[Post New]14 Jun 2007 01:08:23 IST
    Subject: NUMBER THEORy
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THANKS FOR THE SUM
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[Post New]14 Jun 2007 01:09:17 IST
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THE ANS IS 3&5
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[Post New]14 Jun 2007 01:09:45 IST
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WE SEE 3+5=8
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[Post New]14 Jun 2007 01:11:27 IST
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8/2=4=2^2
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[Post New]14 Jun 2007 01:14:08 IST
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EXCEPT 3 ALL PRIMES CAN BE WRITTEN IN THE FORM 6k+or-1
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[Post New]14 Jun 2007 01:18:08 IST
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AS THE NOS 6k+or-2 and 6k+or-3and 6k has more than two factors
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[Post New]14 Jun 2007 01:19:17 IST
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SO TWIN PRIMES ARE 6m+1 and 6m-1
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[Post New]14 Jun 2007 01:21:39 IST
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(p+q)/2=6m
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[Post New]14 Jun 2007 01:27:02 IST
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NOW 6m is a square no
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[Post New]14 Jun 2007 01:27:55 IST
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so m=6a^2
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[Post New]14 Jun 2007 01:28:49 IST
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6m=36a^2
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[Post New]14 Jun 2007 01:31:30 IST
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now p=6m-1=36a^2-1=(6a+1)(6a-1)
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[Post New]14 Jun 2007 01:32:13 IST
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now p=6m-1=36a^2-1=(6a+1)(6a-1) which is not a prime
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[Post New]14 Jun 2007 01:35:26 IST
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THE PRIMES WHICH CANNOT BE EX PRESSED IN 6k+or-form are 2&3.SO ONLY SOL IS 3&5
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