Vipul: Created page with '{{exponential diophantine}} ==Statement== This problem asks for the solutions to: $x^p - y^q = 1$ . Here, $x,y$ are positive integers not equal to $...'$

2009-04-28T22:03:05Z

Created page with '{{exponential diophantine}} ==Statement== This problem asks for the solutions to: <math>x^p - y^q = 1</math>. Here, <math>x,y</math> are positive integers not equal to <math>...'

New page

{{exponential diophantine}}

==Statement==

This problem asks for the solutions to:

<math>x^p - y^q = 1</math>.

Here, <math>x,y</math> are positive integers not equal to <math>0,1</math> and <math>p,q</math> are positive integers greater than <math>1</math>.

[[Catalan's conjecture]] was that the only solutions to this are <math>x = 3, y = 2, p = 2, q = 3</math>. This conjecture has been proved.

Catalan's Diophantine problem - Revision history

Vipul: Created page with '{{exponential diophantine}} ==Statement== This problem asks for the solutions to: x^p - y^q = 1. Here, x,y are positive integers not equal to ...'

Vipul: Created page with '{{exponential diophantine}} ==Statement== This problem asks for the solutions to: $x^p - y^q = 1$ . Here, $x,y$ are positive integers not equal to $...'$