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#1 2012-10-29 16:45:41

John-o
Guest

Diophantine equation

What will be integer solution for x and y-

#2 2012-10-29 17:05:22

bobbym
Administrator

Online

Re: Diophantine equation

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.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

#3 2012-10-29 22:33:21

John-o
Guest

Re: Diophantine equation

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

#4 2012-10-29 23:30:33

bobbym
Administrator

Online

Re: Diophantine equation

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.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

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