Solving a linear equation in a set of integers I

Imre Z. Ruzsa

Acta Arithmetica (1993)

  • Volume: 65, Issue: 3, page 259-282
  • ISSN: 0065-1036

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Imre Z. Ruzsa. "Solving a linear equation in a set of integers I." Acta Arithmetica 65.3 (1993): 259-282. <http://eudml.org/doc/206579>.

@article{ImreZ1993,
author = {Imre Z. Ruzsa},
journal = {Acta Arithmetica},
language = {eng},
number = {3},
pages = {259-282},
title = {Solving a linear equation in a set of integers I},
url = {http://eudml.org/doc/206579},
volume = {65},
year = {1993},
}

TY - JOUR
AU - Imre Z. Ruzsa
TI - Solving a linear equation in a set of integers I
JO - Acta Arithmetica
PY - 1993
VL - 65
IS - 3
SP - 259
EP - 282
LA - eng
UR - http://eudml.org/doc/206579
ER -

References

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  1. M. Ajtai, J. Komlós and E. Szemerédi (1981), A dense infinite Sidon sequence, European J. Combin. 2, 1-11. Zbl0474.10038
  2. F. A. Behrend (1946), On sets of integers which contain no three terms in arithmetical progression, Proc. Nat. Acad. Sci. U.S.A. 32, 331-333. Zbl0060.10302
  3. R. C. Bose (1942), An affine analogue of Singer's theorem, J. Indian Math. Soc. 6, 1-15. Zbl0063.00542
  4. R. C. Bose and S. Chowla (1962-63), Theorems in the additive theory of numbers, Comment. Math. Helv. 37, 141-147. 
  5. P. Erdős and P. Turán (1941), On a problem of Sidon in additive number theory and some related problems, J. London Math. Soc. 16, 212-215. Zbl67.0984.03
  6. H. Halberstam and K. F. Roth (1966), Sequences, Clarendon, London (2nd ed. Springer, New York, 1983). 
  7. D. R. Heath-Brown (1987), Integer sets containing no arithmetic progression, J. London Math. Soc. 35, 385-394. Zbl0589.10062
  8. J. Komlós, M. Sulyok and E. Szemerédi (1975), Linear problems in combinatorial number theory, Acta Math. Hungar. 26, 113-121. Zbl0303.10058
  9. B. Lindström (1969), An inequality for B₂-sequences, J. Combin. Theory 6, 211-212. L. Moser (1953), On non-averaging sets of integers , Canadian J. Math. 5, 245-252. 
  10. K. F. Roth (1953), On certain sets of integers, J. London Math. Soc. 28, 104-109. Zbl0050.04002
  11. J. Singer (1938), A theorem in finite projective geometry and some applications to number theory, Trans. Amer. Math. Soc. 43, 377-385. Zbl64.0972.04
  12. A. Stöhr (1955), Gelöste und ungelöste Fragen über Basen der natürlichen Zahlenreihe, J. Reine Angew. Math. 194, 40-65, 111-140. Zbl0066.03101
  13. E. Szemerédi (1975), On sets of integers containing no k elements in arithmetic progression, Acta Arith. 27, 199-245. Zbl0303.10056
  14. E. Szemerédi (1990), Integer sets containing no arithmetic progressions, Acta Math. Hungar. 56, 155-158. Zbl0721.11007

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