My Math Forum computation problem

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November 24th, 2010, 10:25 AM   #11
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Re: computation problem

Quote:
 Originally Posted by islam i would request ageneral formula for any k
Formula or algorithm? If formula, please define what you mean by "formula" more precisely.

 November 24th, 2010, 10:42 AM #12 Senior Member   Joined: Nov 2010 Posts: 288 Thanks: 1 Re: computation problem aformula with k exoressing how many diffirent even numbers can we make out of k odd numbers by adding every two numbers
November 24th, 2010, 10:48 AM   #13
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Re: computation problem

Quote:
 Originally Posted by islam aformula with k exoressing how many diffirent even numbers can we make out of k odd numbers by adding every two numbers
Yes, but what do you mean by "formula"?
http://en.wikipedia.org/wiki/Closed-form_expression

 November 24th, 2010, 10:51 AM #14 Senior Member   Joined: Nov 2010 Posts: 288 Thanks: 1 Re: computation problem for example right aformula for the sum of the first n natural numbers meanining 1+2+3+.........+n the formula is as u definetly know n(n+1)/2 this is what i mean
November 24th, 2010, 06:19 PM   #15
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Re: computation problem

Quote:
 Originally Posted by islam for example right aformula for the sum of the first n natural numbers meanining 1+2+3+.........+n the formula is as u definetly know n(n+1)/2 this is what i mean
That formula uses only addition and multiplication. What operations will you allow? It's not obvious that a formula exists.

 November 24th, 2010, 09:59 PM #16 Senior Member   Joined: Nov 2010 Posts: 288 Thanks: 1 Re: computation problem thats why i am asking coz i tried to find one i just failed i asked my teacher he didnt know so i thought there might be some genius in this forum who could have gotten some inspiration ..... anyway u think such aformula if existed u think it will help know more about the distribution of prime number by supposing that goldbachs conjecture is true ... i think if it exists we could make astatement equal to reimanns hypothesis it seems it would be even easier than that of reimann...
November 25th, 2010, 11:55 AM   #17
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Re: computation problem

Quote:
 Originally Posted by islam thats why i am asking coz i tried to find one i just failed i asked my teacher he didnt know so i thought there might be some genius in this forum who could have gotten some inspiration ..... anyway u think such aformula if existed u think it will help know more about the distribution of prime number by supposing that goldbachs conjecture is true ... i think if it exists we could make astatement equal to reimanns hypothesis it seems it would be even easier than that of reimann...
Let me take those one at a time.

No, I don't think there is a formula for this, using a typical definition of formula. I think this would be hard to prove, but it's been done -- compare Richardson's theorem or Cherry's improved version of it. My belief in this point is not too strong, though; I could be swayed by an appropriate expert.

If there was such a formula, I don't think that it would yield any additional insight into the prime numbers. In particular, there are too many Goldbach partitions for any given number for this to help at all. I'm fairly sure of this belief.

I'm quite sure that such a formula wouldn't give an easier method to attack the Riemann hypothesis.

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