this is really doing my head in!
I have put up this theory on this link:http://gmatquant.blogspot.com/2010/11/integral-solutions-of-ax-by-c.html
See if it makes sense now.
If there are doubts, get back to me on my blog itself or here...
Interesting post -- makes complete sense. A question though: In your hypothetical question about "- And, a trickier thing to think about - how many integral solutions would 3x - 5y = 42 have?" -- both have to go up, right? So x would have to go up from 14, to 19, to 24 etc. Conversely, y would also go up from 0 to 3, to 6 etc. Neither of those values can be negative since we have the positive integer constraint. Am I correct?
Can you recommend other questions similar to this? Thanks!