Find all solutions that are positive integers of the Diophantine equation:
25x + 35y = 380
Now, this is actually the way you can get the answer to the other problem you posted without guessing.
There is a cool :eek: way to do these using continued fractions but I do not think you number theory course does those until the end of the semester if not at all.
We need to find,
Apply Euclidean algorithm,
Now work backwards,
Multiply by 76,
December 13th 2006, 05:54 PM
oh ok thanks alot :) I thought I was suppost to be looking for exact numbers. Now I understand and see how I could apply this in the previous problem I posted
December 13th 2006, 08:47 PM
Find all solutions that are positive integers of the Diophantine equation: . .
Your answers are correct!
I would write them as: .
December 13th 2006, 09:09 PM
I kind of understand how I got the solutions when I wrote it out the frist time, but how would you apply the solutions to what ThePerfectHacker showed me when he worked it out?
December 14th 2006, 07:57 AM
Here's a really primitive approach . . .
Find all positive integer solutions of: .
Divide by 5: .
This can be written: .
. . Hence: . 
Since is an integer, must some integer . . We have: .