Geodesic
On Divisors of Sums of Integers IV
Canadian journal of mathematics, Tome 40 (1988) no. 4, pp. 788-816

Voir la notice de l'article provenant de la source Cambridge University Press

Throughout this article c 0, c 1, c 2, ... will denote effectively computable positive absolute constants. Denote the cardinality of a set X by |X|. Let N be a positive integer and let A and B be non-empty subsets of {1, ...,N}. Put In [3], Balog and Sá;rközy proved that if N > c 0 and (1) then there exist a 0 and b 0 with a 0 ∊ A 0 and b 0 ∊ B 0 and a prime number p such that and (2) If follows from this result that if |A| ≫ N and |B| ≫ N then there exist a in A and b in B and a prime p such that p 2|(a + b) with 
Sárközy, A.; Stewart, C. L. On Divisors of Sums of Integers IV. Canadian journal of mathematics, Tome 40 (1988) no. 4, pp. 788-816. doi: 10.4153/CJM-1988-035-3
@article{10_4153_CJM_1988_035_3,
     author = {S\'ark\"ozy, A. and Stewart, C. L.},
     title = {On {Divisors} of {Sums} of {Integers} {IV}},
     journal = {Canadian journal of mathematics},
     pages = {788--816},
     year = {1988},
     volume = {40},
     number = {4},
     doi = {10.4153/CJM-1988-035-3},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CJM-1988-035-3/}
}
TY  - JOUR
AU  - Sárközy, A.
AU  - Stewart, C. L.
TI  - On Divisors of Sums of Integers IV
JO  - Canadian journal of mathematics
PY  - 1988
SP  - 788
EP  - 816
VL  - 40
IS  - 4
UR  - http://geodesic.mathdoc.fr/articles/10.4153/CJM-1988-035-3/
DO  - 10.4153/CJM-1988-035-3
ID  - 10_4153_CJM_1988_035_3
ER  - 
%0 Journal Article
%A Sárközy, A.
%A Stewart, C. L.
%T On Divisors of Sums of Integers IV
%J Canadian journal of mathematics
%D 1988
%P 788-816
%V 40
%N 4
%U http://geodesic.mathdoc.fr/articles/10.4153/CJM-1988-035-3/
%R 10.4153/CJM-1988-035-3
%F 10_4153_CJM_1988_035_3

[1] 1. Balog, A. and Sárközy, A., On sums of sequences of integers, I, Acta Arith. 44 (1984), 73–86. Google Scholar

[2] 2. Balog, A. and Sárközy, A., On sums of sequences of integers, If Acta Math. Hung. 44 (1984), 169–179. Google Scholar

[3] 3. Balog, A. and Sárközy, A., On sums of sequences of integers, III, Acta Math. Hung. 44 (1984), 339–349. Google Scholar

[4] 4. Harman, G., Trigonometric sums over primes, I, Mathematika 29 (1981), 249–254. Google Scholar

[5] 5. Iwaniec, H. and Pintz, J., Primes in short intervals, Monatshefte Math. 98 (1984), 115–143. Google Scholar

[6] 6. Montgomery, H. L. and Vaughan, R. C., The large sieve, Mathematika 20 (1973), 119–134. Google Scholar

[7] 7. Pólya, G., Über die Verteilung der quadratischen Reste und Nichtreste, Göttinger Nachrichten (1918), 21–29. Google Scholar

[8] 8. Prachar, K., Primzahlverteilung (Springer-Verlag, 1957). Google Scholar

[9] 9. Sárközy, A. and Stewart, C. L., On divisors of sums of integers, II, J. reine angew Math. 365 (1986), 171–191. Google Scholar

[10] 10. Sárközy, A. and Stewart, C. L., On exponential sums over prime numbers, J. Austral. Math. Soc. Series A, to appear. Google Scholar | DOI

[11] 11. Vinogradov, I. M., An asymptotic equality in the theory of quadratic forms, Zh. fiz.-matem. Obshch. Permsk universitet 1 (1918), 18–28. Google Scholar

Cité par Sources :