Some Applications of a Theorem of M. Kneser.

AbstractA Theorem of M. Kneser relating densities of sumsets to densities of their summands (see [H. Halberstam and K. F. Roth, "Sequences," Chap. 1. Oxford Univ. Press, Oxford], 1966]) is used to set up a machine for settling questions regarding the generalized form of Waring′s problem in additive number theory. For example, if a strictly increasing sequence of integers represents all sufficiently large integers by ternary sums, and an element is removed from the sequence such that the terms remaining represent all sufficiently large integers by sums of some fixed number of terms, then that fixed number is at most seven and this result is best possible