• Corpus ID: 11969516

ON DIFFERENCE SETS OF SEQUENCES OF INTEGERS . III

@inproceedings{Saricozy1978ONDS,
  title={ON DIFFERENCE SETS OF SEQUENCES OF INTEGERS . III},
  author={A. Saricozy},
  year={1978}
}
where the maximum is taken for those sets ul< u~-K.. , which form an &‘-set relative to the set 12, 22, . . . , n2, . . . . see [ll].) In the case of the arithmetic progressions of three terms, we may use the following simple fact: (i) A set afqrr,, afqu,, “,. , afqu, (where a is an integer and t, q, ul, u2, . . . , u, are positive integers) does not contain an arithmetic progression of three terms if and only if also the set u,, u,, . . . , U, has this property. 
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References

SHOWING 1-10 OF 22 REFERENCES
The exceptional set in Goldbach''s problem
An electromagnetic release device for cameras which may selectively be operated continuously comprises a motor circuit, a first switching means adapted to turn the motor circuit on or off, a stopper
Sur quelques ensembles d’entiers
  • fomptes Rendus, 234
  • 1952
ROTH, lrregularities of sequences relative to arithmetic progressions, I-IV
  • Marh. Ann,,
  • 1967
ROT~, On certain sets of integers,
  • London Math. Soc.,
  • 1953
VAUGHAN, The exceptional set in Goldbach’s problem, Acta Arithmetica
  • 1975
ROTH, Iil:egularities of sequences relative to arithmetic progressions
  • I--IV, _Math. Ann.,
  • 1967
...
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