A generalization of Fermat's last theorem which states that if ,
where ,
, , , , and are any positive integers
with ,
then ,
, and have a common factor. The conjecture was announced in Mauldin
(1997), and a cash prize of has been offered for its proof or a counterexample
(Castelvecchi 2013).
This conjecture is more properly known as the Tijdeman-Zagier conjecture (Elkies 2007).
Brun, V. "Über hypothesesenbildungen." Arc. Math. Naturvidenskab34, 1-14, 1914.Castelvecchi, D. "Mathematics
Prize Ups the Ante to $1 Million." June 4, 2013. http://blogs.nature.com/news/2013/06/mathematics-prize-ups-the-ante-to-1-million.html.Darmon,
H. and Granville, A. "On the Equations and ." Bull. London Math. Soc.27,
513-543, 1995.Elkies, N. "The ABCs of Number Theory." Harvard
Math. Rev.1, 64-76, 2007.Mauldin, R. D. "A Generalization
of Fermat's Last Theorem: The Beal Conjecture and Prize Problem." Not. Amer.
Math. Soc.44, 1436-1437, 1997.Mauldin, R. D. "The
Beal Conjecture and Prize." http://www.math.unt.edu/~mauldin/beal.html.