Abstract
For a natural number k≥ 2 letρ=ρ(k) be the smallest natural number which does not dividek− 1. We show that for any subset A of a right cancellative semigroup S which contains no solutions of the equation x1+⋯ +xk=y there is an element s inS such that the setsA, A+s, . ,A + (ρ− 1)sare pairwise disjoint. In particular, if S is finite, such a set A has at most | S |/ρ elements. This estimate is sharp.
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