is it true?

what is the proof?

I prefer a hint if it ain't difficult to prove.

tnx :)

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- May 28th 2006, 04:44 AMsrulikbdFor all primes greater than 3, p = 6ką1?
is it true?

what is the proof?

I prefer a hint if it ain't difficult to prove.

tnx :) - May 28th 2006, 05:05 AMCaptainBlackQuote:

Originally Posted by**srulikbd**

Let be a prime. Consider the possible values of the remainder

when is divided by . As is prime the remainder cannot

be divisible by any factor of .

RonL - May 28th 2006, 06:30 AMsrulikbdOk Understood
quite easy :)

- May 28th 2006, 10:55 AMThePerfectHacker
Or to say it another way.

Any number must have form,

Note that,

are all divisible by 2 and thus not a prime.

And that,

is divisble by 3 and thus not a prime.

Hence the only possibilites are,

or,

Thus,

for some integer . - May 29th 2006, 01:30 AMsrulikbdanother question
how do I prove that there are infinite primes that have the form xk+y, y<x, and share no common factors?

- May 29th 2006, 11:19 AMThePerfectHackerQuote:

Originally Posted by**srulikbd**

That is too complicated I believe the proof use's funtional analysis. It was first proven by Dirichelt (my avatar :)).

In fact in the book "Introduction to Theory of Numbers" by Hardy and Wright. Which contains elementary,algebraic and analytic number theory; proves all theorems in the book (even the prime number theorem) except this theorem! That is how complicated it is. - May 31st 2006, 10:28 AMsrulikbdcool
coincidence :)

- May 31st 2006, 03:58 PMThePerfectHacker
I can present a proof to why are there infinitely many primes of form if you really wish to know.

- Jun 1st 2006, 12:45 AMsrulikbdok
i'll be happy!

- Jun 1st 2006, 10:02 AMThePerfectHackerQuote:

Originally Posted by**srulikbd**

*Lemma:*The product of integers of the form is again an integer of the form .

*Proof:*: If and then, . Q.E.D.

*Theorem*: There are infinitely many primes of form .

*Proof:*Assume there are finitely many primes of form call them . Then form an integer,

Prime factorize as,

Note that because it is odd. Thus, for any .

We cannot have that all the primes factors of are of the form for that would imply that has form , which is does not because by the lemma. Thus one of its factors has form . Because an odd prime has one of two forms . But then thus, thus, , because is found among thus an impossibility. Q.E.D. - Jun 2nd 2006, 01:04 AMsrulikbd
I didn't understand the end-what does | means?

and whaat does X means? (2X...) does it means doesn't divide?

tnx :) - Jun 2nd 2006, 05:25 AMCaptainBlackQuote:

Originally Posted by**srulikbd**

is to be read as does not divide .

RonL - Jun 2nd 2006, 07:10 AMsrulikbdtnx both of u now I understand
:)