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We study the attractive SU($N$) Hubbard model with particle-hole symmetry.The model is defined on a bipartite lattice with the number of sites $N_A$$(N_B)$ in the $A$ $(B)$ sublattice. We prove three theorems that allow us toidentify the basic ground-state properties: the degeneracy, the fermion number,and the SU($N$) quantum number. We also show that the ground state exhibitscharge density wave order when $|N_A-N_B|$ is macroscopically large. Thetheorems hold for a bipartite lattice in any dimension, even withouttranslation invariance.

Rigorous results on the ground state of the attractive SU($N$) Hubbard model