On the number of monochromatic solutions of x+y=z2

Combinatorics Probability and Computing

Volumn 15, Issue 1-2, 2006, Pages 213-227

  Khalfalah, Ayman ^a   Szemerédi, Endre ^b  

^a Alexandria University The Faculty Of Engineering   (Egypt)

^b RUTGERS UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

DIFFERENTIAL EQUATIONS; INTEGER PROGRAMMING;

INTEGER COEFFICIENT;

POLYNOMIALS;

EID: 29744452866     PISSN: 09635483     EISSN: 14692163     Source Type: Journal    
DOI: 10.1017/S0963548305007169     Document Type: Article

References (9)

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3. Khalfalah, A. A., Lodha, S. P. and Szemerédi, E. (2002) Tight bound for the density of sequence of integers the sum of no two of which is a perfect square. Discrete Math., 256 243-255.
4. Lagarias, J. P., Odlyzko, A. M. and Shearer, J. B. (1982) On the density of sequences of integers the sum of no two of which is a square I : arithmetic progressions. J. Combin. Theory Ser. A 33 167-185.
5. Lagarias, J. P., Odlyzko, A. M. and Shearer, J. B. (1983) On the density of sequences of integers the sum of no two of which is a square II: general sequences. J. Combin. Theory Ser. A 34 123-139.
6. Massias, J. P. Sur les suites dont les sommes des terms 2 á 2 ne sont par des carrés.
7. Sárközy, A. (1978) On difference sets of sequences of integers I. Acta Math. Acad. Sci. Hungar. 31 125-149.
8. Vaughan, R. C. (1997) The Hardy-Littlewood Method, 2nd edition, Cambridge University Press.
9. Vinogradov, I. M. (1977) The Method of Trigonometrical Sums in the Theory of Numbers, Interscience Publishers. Translated from the Russian, revised and annotated by K. F. Roth and Anne Davenport.