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On Divisors of Sums of Integers IV

Published online by Cambridge University Press:  20 November 2018

A. Sárközy  and
C. L. Stewart
A. Sárközy
Affiliation:
Hungarian Academy of Science, Budapest, Hungary
C. L. Stewart
Affiliation:
University of Waterloo, Waterloo, Ontario
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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

Information

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 40 , Issue 4 , 01 August 1988 , pp. 788 - 816
Copyright
Copyright © Canadian Mathematical Society 1988

References

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