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#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.
90% of mathematicians do not understand 90% of currently published mathematics.
I am willing to wager that over 75% of the new words that appeared were nothing more than spelling errors that caught on.
#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.
90% of mathematicians do not understand 90% of currently published mathematics.
I am willing to wager that over 75% of the new words that appeared were nothing more than spelling errors that caught on.