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**John-o****Guest**

What will be integer solution for x and y-

**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 86,302

Hi John-o;

There are a lot of solutions to that equation. Are there any constraints you have left out?

We can treat this with a few more constraints as an Egyptian fraction. One possible solution is

So we have a=1 and ab -1 =14 and b = 15

Substituting into the top equation:

x = 15 , y = 210 is one solution.

There 5 solutions with positive integers and x ≠ y. They are

For a general solution that gets all solutions

All solutions are now generated by adding 14 to the divisors of 196.

**In mathematics, you don't understand things. You just get used to them.Of course that result can be rigorously obtained, but who cares?Combinatorics is Algebra and Algebra is Combinatorics.**

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**John-o****Guest**

What is this egyptian fraction?I'd like to know about it.

**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 86,302

Hi;

This is where it is explained:

http://en.wikipedia.org/wiki/Egyptian_fraction

if you have a problem with understanding it post it here.

**In mathematics, you don't understand things. You just get used to them.Of course that result can be rigorously obtained, but who cares?Combinatorics is Algebra and Algebra is Combinatorics.**

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