TOPICS
Search

Beal's Conjecture

A generalization of Fermat's last theorem which states that if a^x+b^y=c^z, where a, b, c, x, y, and z are any positive integers with x,y,z>2, then a, b, and c have a common factor. The conjecture was announced in Mauldin (1997), and a cash prize of $1000000 has been offered for its proof or a counterexample (Castelvecchi 2013).

This conjecture is more properly known as the Tijdeman-Zagier conjecture (Elkies 2007).

See also

abc Conjecture, Fermat-Catalan Conjecture, Fermat's Last Theorem

Explore with Wolfram|Alpha

References

Brun, V. "Über hypothesesenbildungen." Arc. Math. Naturvidenskab 34, 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 z^m=F(x,y) and Ax^p+By^q=cZ^r." 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.

Cite this as:

Weisstein, Eric W. "Beal's Conjecture." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/BealsConjecture.html

Subject classifications