where C is an absolute constant. A similar result had previously been obtained by the author with the condition ai \nmid ajak. The proof, in typical Erdös style, is based on a combinatorial lemma couched in graph theoretic language. This lemma gives an upper bound in terms of t, and t2 for the number of edges in a graph G containing no circuit of four edges and with t vertices, x1, ... ,xt, each edge being incident to one of the vertices xi, 1 \leq i < t2 < t1.
Classif.: * 11B83 Special sequences of integers and polynomials
11B75 Combinatorial number theory
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