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#1 2006-10-10 04:35:15

hmm_marie
Member
Registered: 2006-10-09
Posts: 7

prime numbers

hey... i have another tough one here... i hope someone can help me... smile

so one has to find all possible positive full (=whole?) numbers for n, for which 6n²+5n-4 is a prime number.

so far i factorised the term to make 6 (n - (1/2)) * (n + (4/3)) has to be eual to the prime number.

now i thought that as soon as one of the factors was equal to "1" then the other factor would have to be equal to the actual rime number itsself. and that would obvieously make the solution a prime number. as 1 * p = p

when (n + (4/3)) = 1 then n =-(1/3)
when (n - (1/2)) =1 then n = 1/2
but if one has to take the "6" into consideration? then 6 (n - (1/2)) = 1 then n = 2/3 etc......
but these are NOT positive full/numbers?!?!? as they are supposed to be in the question.

but if one takes the quation from the question and tries it out and puts in lets say n=1 then 6*1² + 5*1 - 4=7 which is a rime number.

oh i dont get it. can anyone help me? whats n and how do i prove it?

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#2 2006-10-10 16:37:29

John E. Franklin
Member
Registered: 2005-08-29
Posts: 3,588

Re: prime numbers

I'll start where you factored it, but distribute the 2 and the 3 from the 6 because 2 * 3 = 6.
6 (n - (1/2)) * (n + (4/3))

(2n - 1) * (3n + 4)

If (2n - 1) = 1, then it could be prime and that is the case you found with n = 1, and then you get 7.

For all other counting numbers, the two things being (2n - 1) and (3n + 4) are multiplied, and both of them
are odd counting numbers, so the product has two factors we know of immediately, so they are not prime for n > 1.

Cool !, Huh?


igloo myrtilles fourmis

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#3 2006-10-11 01:23:17

hmm_marie
Member
Registered: 2006-10-09
Posts: 7

Re: prime numbers

yaaaaayy!!! cool, thank you:):) sooooo much

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