Let there be three polynomials , , and with no common factors such that
Then the number of distinct roots of the three polynomials is one or more greater than their largest degree. The theorem was first proved by
Mason's theorem may be viewed as a very special case of a Wronskian estimate (Chudnovsky and Chudnovsky 1984). The corresponding Wronskian identity in the proof by Lang (1993) is
so if ,
, and are linearly dependent, then so are and . More powerful Wronskian estimates with applications
toward Diophantine approximation of solutions of linear differential equations may
be found in Chudnovsky and Chudnovsky (1984) and Osgood (1985).
Chudnovsky, D. V. and Chudnovsky, G. V. "The Wronskian Formalism for Linear Differential Equations and Padé Approximations."
Adv. Math.53, 28-54, 1984.Dubuque, W. "poly FLT,
abc theorem, Wronskian formalism [was: Entire solutions of f^2+g^2=1]." email@example.com
posting, Jul 17, 1996.Lang, S. "Old and New Conjectured Diophantine
Inequalities." Bull. Amer. Math. Soc.23, 37-75, 1990.Lang,
3rd ed. Reading, MA: Addison-Wesley, 1993.Mason, R. C.
Equations over Functions Fields. Cambridge, England: Cambridge University
Press, 1984.Osgood, C. F. "Sometimes Effective Thue-Siegel-Roth-Schmidt-Nevanlinna
Bounds, or Better." J. Number Th.21, 347-389, 1985.Stothers,
W. W. "Polynomial Identities and Hauptmodulen." Quart. J. Math.
Oxford Ser. II32, 349-370, 1981.