Beal’s Conjuncture

One of this days I come across the Bael’s conjuncture and the Bael’s Prize.

The conjecture is a generalization of Fermat’s Last Theorem, that states:

If

,

where and are positive integers with , then and have a common prime factor.

This is still a conjecture, meaning that it was not proved or disproved. And that got me thinking, because it doesn’t seemed that hard of a problem. It didn’t take long for that to turn into a dialog between the (ex-)Math student me and the programmer me.

The programmer said that all it takes is a script to test a decent chunk of all the possible combinations until you find a case that doesn’t satisfy the needed requisites, while the math student argued that that would only work if the conjecture was not true, because you can’t brute force a math prove for .

Which is true. The only way to truly prove that the conjecture is valid (and making it a theorem) is going through one of the several methodologies mathematics define for this.

This is, maybe, something for a day I feel really bored. And most likely the programmer will win and try to find a counter-example first.

Source: theMage