On sets of natural numbers without solution to a noninvariant linear equation

ArticleOriginal scientific text

Title

Authors ¹

Mathematisches Seminar, Universität zu Kiel, Ludewig-Meyn-Str. 4, 24098 Kiel, Germany

N. Alon, Independent sets in regular graphs and sum-free sets of finite groups, Israel J. Math. 73 (1991), 247-256.
J.-M. Deshoulliers, G. Freimen, V. Sós and M. Temkin, On the structure of sum-free sets, 2, Astérisque 258 (1999), 149-161.
P. Erdős, V. Sós and A. Sárközy, On sum sets of Sidon sets, J. Number Theory 47 (1993), 329-347.
V. Lev, Optimal representation by sumsets and subset sums, ibid. 62 (1997), 127-143.
T. Łuczak and T. Schoen, On the infinite sum-free sets of natural numbers, ibid. 66 (1997), 211-224.
K. F. Roth, On certain sets of integers, J. London Math. Soc. 28 (1953), 104-109.
I. Z. Ruzsa, On infinite Sidon sequences, J. Number Theory 68 (1998), 63-71.
I. Z. Ruzsa, Solving a linear equation in a set of integers I, Acta Arith. 65 (1993), 259-282.
I. Z. Ruzsa, Solving a linear equation in a set of integers II, ibid. 72 (1995), 385-397.
T. Schoen, On the density of universal sum-free sets, Combin. Probab. Comput. 8 (1999), 277-280.
T. Schoen, Subsets of {1,...,n} with no solutions to the equation x+y = kz, in preparation.