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Fuzzy Dark Matter (FDM) has recently emerged as an interesting alternativemodel to the standard Cold Dark Matter (CDM). In this model, dark matterconsists of very light bosonic particles with quantum mechanical effects ongalactic scales. Using the N-body code AX-GADGET, we perform cosmologicalsimulations of FDM that fully model the dynamical effects of the quantumpotential throughout cosmic evolution. Through the combined analysis of FDMvolume and high-resolution zoom-in simulations of different FDM particle masses($m_{\chi}$ $\sim$ $10^{-23} - 10^{-21}$ eV/c$^2$), we study how FDM impactsthe abundance of substructure and the inner density profiles of dark matterhaloes. For the first time, using our FDM volume simulations, we provide afitting formula for the FDM-to-CDM subhalo abundance ratio as a function of theFDM mass.  More importantly, our simulations clearly demonstrate that there exists anextended FDM particle mass interval able to reproduce the observed substructurecounts and, at the same time, create substantial cores ($r_{c} \sim 1$ kpc) inthe density profile of dwarf galaxies ($\approx 10^{9}-10^{10}$ M$_{\odot}$),which stands in stark contrast with CDM predictions even with baryonic effectstaken into account. The dark matter distribution in the faintest galaxiesoffers then a clear way to discriminate between FDM and CDM.

No Catch-22 for Fuzzy Dark Matter: testing substructure counts and core sizes via high-resolution cosmological simulations