# .

The Mason–Stothers theorem, or simply Mason's theorem, is a mathematical theorem about polynomials, analogous to the abc conjecture for integers. It is named after W. Wilson Stothers, who published it in 1981, and R. C. Mason, who rediscovered it shortly thereafter.

The theorem states:

Let a(t), b(t), and c(t) be relatively prime polynomials such that a + b = c, with coefficients that are either real numbers or complex numbers. Then

$$\max\{\deg(a),\deg(b),\deg(c)\} \le \deg(\operatorname{rad}(abc))-1,$$

where rad(f) is the polynomial of minimum degree that has the same roots as f, so deg(rad(f)) gives the number of distinct roots of f.

References

Stothers, W. W. (1981), "Polynomial identities and hauptmoduln", Quarterly J. Math. Oxford, 2 32: 349–370, doi:10.1093/qmath/32.3.349.
Mason, R. C. (1984), Diophantine Equations over Function Fields, London Mathematical Society Lecture Note Series 96, Cambridge, England: Cambridge University Press.

Lang, Serge (2002). Algebra. New York, Berlin, Heidelberg: Springer-Verlag. p. 194. ISBN 0-387-95385-X.