Thread: Simple Diophantine equation View Single Post
2009-04-10, 11:32   #4
R.D. Silverman

Nov 2003

161008 Posts

Quote:
 Originally Posted by Batalov $a^3 = b^5 + 100$ Is there more than one solution? ________ P.S. Argh, I only started playing with modular restrictions, and you've already looked up to 10^35. If so, then of course I am convinced, too. Sorry, then it was ...too simple.

Note that Faltings proof of the Mordell Conjecture shows that there
are only finitely many solutions. Actually, this is like hitting a thumbtack
with a sledgehammer. Siegel's Theorem suffices to show the same thing.

Unfortunately, neither is effective. Nor would an application of the
ABC conjecture be effective.