Discussion about math, puzzles, games and fun. Useful symbols: ÷ × ½ √ ∞ ≠ ≤ ≥ ≈ ⇒ ± ∈ Δ θ ∴ ∑ ∫ π -¹ ² ³ °

You are not logged in.

- Topics: Active | Unanswered

Pages: **1**

**ReallyConfused****Guest**

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****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 104,747

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.****If it ain't broke, fix it until it is.** **A number by itself is useful, but it is far more useful to know how accurate or certain that number is.**

Offline

**ReallyConfused****Guest**

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

**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 104,747

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.****If it ain't broke, fix it until it is.** **A number by itself is useful, but it is far more useful to know how accurate or certain that number is.**

Offline

**nope****Guest**

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****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 104,747

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.****If it ain't broke, fix it until it is.** **A number by itself is useful, but it is far more useful to know how accurate or certain that number is.**

Offline

Pages: **1**