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Let $(M^n,g)$ be a closed Riemannian manifold and $g_E$ the Euclidean metric. We show that for $m>1$, $\left(M^n\times {𝐑}^m,(g+g_E)\right)$ is not conformal to a positive Einstein manifold. Moreover, $\left(M^n\times {𝐑}^m,(g+g_E)\right)$ is not conformal to a Riemannian manifold of positive Ricci curvature, through a radial, integrable, smooth function, $\varphi :{𝐑}^{𝐦}\to {𝐑}^{+}$, for $m>1$. These results are motivated by some recent questions on Yamabe constants.