On Divisors of Sums of Integers IV
Andràs Sárközy, Cameron L. Stewart · Canadian Journal of Mathematics · 1988
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