### A basis of ℤₘ, II

Given a set A ⊂ ℕ let ${\sigma}_{A}\left(n\right)$ denote the number of ordered pairs (a,a’) ∈ A × A such that a + a’ = n. Erdős and Turán conjectured that for any asymptotic basis A of ℕ, ${\sigma}_{A}\left(n\right)$ is unbounded. We show that the analogue of the Erdős-Turán conjecture does not hold in the abelian group (ℤₘ,+), namely, for any natural number m, there exists a set A ⊆ ℤₘ such that A + A = ℤₘ and ${\sigma}_{A}\left(n\u0305\right)\le 5120$ for all n̅ ∈ ℤₘ.