If Coulomb’s law involved 1/r3 dependence (instead of 1/r2), would Gauss’s law be still true?
In this case the the electric field due to point charge q is E=r2kq Now consider a gaussian surface as a sphere surface of radius r The flux through the surface is ϕ=∮E.dS=(kq/r3)∮dS=kq/r3×4πr2=r4πkq Thus this flux is dependent on r but from Gauss's law the flux depends only on the charge inside the surface.
