Let be a finite set of integers such that the -fold sumset is “small”, i.e., for some constant . There exists an -dimensional arithmetic progression (http://planetmath.org/MulidimensionalArithmeticProgression) of length that contains , and such that and are functions of only.
- 1 Melvyn B. Nathanson. Additive Number Theory: Inverse Problems and Geometry of Sumsets, volume 165 of GTM. Springer, 1996. http://www.emis.de/cgi-bin/zmen/ZMATH/en/quick.html?type=html&an=0859.11003Zbl 0859.11003.