Roth's Theorem

For algebraic 

with , has finitely many solutions. Klaus Roth received a Fields medal for this result.

REFERENCES:

Cassels, J. W. S. An Introduction to Diophantine Approximations. Cambridge, England: Cambridge University Press, 1957.

Davenport, H. and Roth, K. F. "Rational Approximations to Algebraic Numbers." Mathematika 2, 160-167, 1955.

Roth, K. F. "Rational Approximations to Algebraic Numbers." Mathematika 2, 1-20, 1955.

Roth, K. F. "Corrigendum to 'Rational Approximations to Algebraic Numbers.' " Mathematika 2, 168, 1955.