Roth's theorem
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There are two major results of Klaus Roth in mathematics which go by the name of "Roth's theorem":
- The Thue-Siegel-Roth theorem in Diophantine approximation, which concerns the rarity to which an irrational algebraic number can be approximated by a rational number; and
- Roth's theorem in arithmetic combinatorics, which is a special case of Szemeredi's theorem and asserts that any set of natural numbers with positive density will contain infinitely many arithmetic progressions of length three.