**Peter Norvig** 22 October 2015, revised 28 October 2015

# Beal's Conjecture Revisited2¶

In 1637, Pierre de Fermat wrote in the margin of a book that he had a proof of his famous "Last Theorem":

If $A^n + B^n = C^n$,
where $A, B, C, n$ are positive integers
then $n \le 2$.

Centuries passed before Andrew Beal, a businessman and amateur mathematician, made his conjecture in 1993:

If $A^x + B^y = C^z$,
where $A, B, C, x, y, z$ are positive integers and $x, y, z$ are all greater than $2$,
then $A, B$ and $C$ must have a common prime factor.

# Conclusion¶

This was fun, but I can't recommend anyone spend a serious amount of computer time looking for counterexamples to the Beal Conjecture—the money you invest in computer time would be more than the expected value of your prize winnings. I suggest you work on a proof rather than a counterexample, or work on some other interesting problem instead!