Catalan's conjecture: Difference between revisions

Revision as of 22:03, 28 April 2009

This conjecture states that the solution set to Catalan's Diophantine problem:

$x^{p}-y^{q}=1$ ,

for $x,y$ positive integers not equal to $0,1$ and $p,q$ positive integers greater than one, has precisely one solution: $x=3,y=2,p=2,q=3$ .

The conjecture has been proved.

@@ Line 5: / Line 5: @@
 <math>x^p - y^q = 1</math>,
-for <math>x,y \ne 0,1</math> and <math>p,q</math> positive integers greater than one, has ''precisely'' one solution: <math>x = 3, y = 2, p = 2, q = 3</math>.
+for <math>x,y</math> positive integers not equal to <math>0,1</math> and <math>p,q</math> positive integers greater than one, has ''precisely'' one solution: <math>x = 3, y = 2, p = 2, q = 3</math>.
 The conjecture has been proved.