Abstract
Given a set AN letA(n) denote the number of ordered pairs (a,a ' ) 2 A×A such that a+a ' = n. Erdýos and Turan conjectured that for any asymptotic basis A of N, �A(n) is unbounded. We show that the analogue of the Erdýos-Turan conjecture does not hold in the abelian group (Zm,+), namely, for any natural number m, there exists a set AZm such that A + A = Zm andA(n) � 5120 for all n 2 Zm.
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