Abstract
Freiman’s 2.4-Theorem states that any set A⊂ℤ p satisfying |2A|≤2.4|A|-3 and |A|<p/35 can be covered by an arithmetic progression of length at most |2A|-|A|+1. A more general result of Green and Ruzsa implies that this covering property holds for any set satisfying |2A|≤3|A|-4 as long as the rather strong density requirement |A|<p/10 215 is satisfied. We present a version of this statement that allows for sets satisfying |2A|≤2.48|A|-7 with the more modest density requirement of |A|<p/10 10 .
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