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#1 2012-10-30 20:24:30
- ReallyConfused
- Guest
Integer solution of this equation
How can I find integer solutions of this,
I know there is a solution for all n,I searched in wikipedia,and I didn't find a suitable solution.could you please explain how to solve.#2 2012-10-30 20:33:42
- bobbym
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Re: Integer solution of this equation
Hi ReallyConfused;
If x>0 and y>0 and z>0 then as far as I know there are only computer solutions. It is an open problem
http://en.wikipedia.org/wiki/Erd%C5%91s … conjecture
http://en.wikipedia.org/wiki/Egyptian_fraction
whether there is a solution for all n.
Sometimes it can be solved, for instance when
then a solution is:
In mathematics, you don't understand things. You just get used to them.
Probability is the most important concept in modern science, especially as nobody has the slightest notion what it means.
90% of mathematicians do not understand 90% of currently published mathematics.
#3 2012-10-30 23:03:37
- ReallyConfused
- Guest
Re: Integer solution of this equation
That is the thing,I want a method that will work for any n.
#4 2012-10-31 00:02:17
- bobbym
- Administrator
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Re: Integer solution of this equation
Hi ReallyConfused;
That is the thing,I want a method that will work for any n.
Those two sites are saying the mathematical method does not yet exist. If it did this would not be an open question. It can be done by computer though.
There are solutions if you can work with positive and negative numbers. You have not told me what constraints there are on the problem.
In mathematics, you don't understand things. You just get used to them.
Probability is the most important concept in modern science, especially as nobody has the slightest notion what it means.
90% of mathematicians do not understand 90% of currently published mathematics.
#5 2012-11-05 12:35:57
- nope
- Guest
Re: Integer solution of this equation
There are not integer solutions for all n, take for example
, then and since the biggest values for the 3 fractions are when then there are no solutions to the problem for n=1#6 2012-11-05 15:16:06
- bobbym
- Administrator
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Re: Integer solution of this equation
Hi Nope;
I think he knows that he was for looking for a method for the ones that do have solutions.
In mathematics, you don't understand things. You just get used to them.
Probability is the most important concept in modern science, especially as nobody has the slightest notion what it means.
90% of mathematicians do not understand 90% of currently published mathematics.