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

Acta Arithmetica (2000)

- Volume: 93, Issue: 2, page 149-155
- ISSN: 0065-1036

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topTomasz Schoen. "On sets of natural numbers without solution to a noninvariant linear equation." Acta Arithmetica 93.2 (2000): 149-155. <http://eudml.org/doc/207406>.

@article{TomaszSchoen2000,

author = {Tomasz Schoen},

journal = {Acta Arithmetica},

keywords = {linear equations; combinatorial number theory},

language = {eng},

number = {2},

pages = {149-155},

title = {On sets of natural numbers without solution to a noninvariant linear equation},

url = {http://eudml.org/doc/207406},

volume = {93},

year = {2000},

}

TY - JOUR

AU - Tomasz Schoen

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

JO - Acta Arithmetica

PY - 2000

VL - 93

IS - 2

SP - 149

EP - 155

LA - eng

KW - linear equations; combinatorial number theory

UR - http://eudml.org/doc/207406

ER -

## References

top- [1] N. Alon, Independent sets in regular graphs and sum-free sets of finite groups, Israel J. Math. 73 (1991), 247-256. Zbl0762.05050
- [2] J.-M. Deshoulliers, G. Freimen, V. Sós and M. Temkin, On the structure of sum-free sets, 2, Astérisque 258 (1999), 149-161.
- [3] P. Erdős, V. Sós and A. Sárközy, On sum sets of Sidon sets, J. Number Theory 47 (1993), 329-347. Zbl0811.11014
- [4] V. Lev, Optimal representation by sumsets and subset sums, ibid. 62 (1997), 127-143. Zbl0868.11017
- [5] T. Łuczak and T. Schoen, On the infinite sum-free sets of natural numbers, ibid. 66 (1997), 211-224. Zbl0884.11018
- [6] K. F. Roth, On certain sets of integers, J. London Math. Soc. 28 (1953), 104-109. Zbl0050.04002
- [7] I. Z. Ruzsa, On infinite Sidon sequences, J. Number Theory 68 (1998), 63-71. Zbl0927.11005
- [8] I. Z. Ruzsa, Solving a linear equation in a set of integers I, Acta Arith. 65 (1993), 259-282. Zbl1042.11525
- [9] I. Z. Ruzsa, Solving a linear equation in a set of integers II, ibid. 72 (1995), 385-397. Zbl1044.11617
- [10] T. Schoen, On the density of universal sum-free sets, Combin. Probab. Comput. 8 (1999), 277-280. Zbl0936.11015
- [11] T. Schoen, Subsets of {1,...,n} with no solutions to the equation x+y = kz, in preparation.

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