Math Is Fun Forum

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.

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

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:

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In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

ReallyConfused

Guest

Re: Integer solution of this equation

That is the thing,I want a method that will work for any n.

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

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.

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In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

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

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

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.

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In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.