# Catalan's conjecture [closed]

can you generalize the method of solving the equation of the type $2^x$ + $19^y$ = $z^2$ has a solution (3, 0, 3). Also, $8^x$ + $19^y$ = $z^2$ has no solution. But, $8^x$ + $17^y$ = $z^2$ has a solution (2, 1, 9). I think these there are very close to each other in means of prime base of each y term.

What is the important role by Catalan conjecture in this questions. Instead of trail and error can we write some general solutions of those equations. Can you discuss...plz?

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The @ does not work like this; you may want to log into whatever account you used for your previous question, and ask this in a comment to the answer you refer to. You should not begin a new question to engage in discussion with another user regarding their answer to a previous question. –  Arturo Magidin Mar 21 '12 at 4:23
Your title has two typos in two words: that's usually a bad idea... Please, do not address questions to specific users: if you spend five minutes browsing the site, you will notice that that is not how this site operates. (We do not write plZ here, by the way!) –  Mariano Suárez-Alvarez Mar 21 '12 at 4:24
For those who wonder... –  t.b. Mar 21 '12 at 4:24
Thanks t.b. I did wonder. –  mixedmath Mar 21 '12 at 4:25
@Adam: Done. Anyone can still see the original post by visiting the revision history. I'll delete my previous comment, and this one after you see it (maybe "upvote" this comment so I know?) –  The Chaz 2.0 Mar 22 '12 at 15:02
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## closed as too localized by Arturo Magidin, Alex B., Asaf Karagila, t.b., The Chaz 2.0Mar 22 '12 at 15:00

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2. I don't think the Catalan equation $x^m-y^n=1$ has much to do with the equations you ask about. What makes you think it has an "important role"?