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In mathematics, Freiman's theorem is a combinatorial result in number theory. It in a sense accounts for the approximate structure of sets of integers which contain a high proportion of their internal sums, taken two at a time. The formal statement is. Let A be a finite set of integers such that the sumset A + A is small, in the sense that A + A < cA for some constant c. There exists an ndimensional arithmetic progression of length c′A that contains A, and such that c′ and n depend only on c. This result is due to G. A. Freiman (1966). Much interest in it, and applications, stemmed from a new proof by Imre Ruzsa. References * Melvyn B. Nathanson, Additive Number Theory: Inverse Problems and Geometry of Sumsets volume 165 of GTM. Springer, 1996. Zbl 0859.11003. Retrieved from "http://en.wikipedia.org/"

