View source for User:Noosfractal/Beal's Conjecture

While investigating mathematical forms associated with [[Fermat's last theorem]], [[Andrew Beal]] noticed a remarkable pattern, leading him to [[conjecture]]:


:'''Beal's conjecture''': if ''x''<sup>''m''</sup> + ''y''<sup>''n''</sup> = ''z''<sup>''r''</sup>, where ''m'', ''n'', ''r'', ''x'', ''y'' and ''z'' are [[negative and non-negative numbers|positive]] [[integer|integers]] with ''m'', ''n'', ''r'' > 2, then ''x'', ''y'' and ''z'' must have a common [[prime factor]].


For example, the solution 3<sup>3</sup> + 6<sup>3</sup> = 3<sup>5</sup> has bases with a common factor of 3, and the solution 7<sup>6</sup> + 7<sup>7</sup> = 98<sup>3</sup> has bases with a common factor of 7.  As of 2005, there are no known [[counterexample|counterexamples]].

A reward of $100,000 is offered for a proof or disproof of the conjecture.

=== References ===
* http://www.bealconjecture.com/
* A search for counterexamples - http://www.norvig.com/beal.html
* http://planetmath.org/encyclopedia/BealsConjecture.html