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In this paper we show that for any $k\geq2$, there exist two universalconstants $C_k,D_k>0$, such that for any finite subset $A$ of positive realnumbers with $|AA|\leq M|A|$, $|kA|\geq\frac{C_k}{M^{D_k}}\cdot|A|^{\log_42k}.$

Multi-fold sums from a set with few products