Consider an attractive central force of the form F(r)=−krn,k is a constant. For a stable circular orbit to exist.

F(r)=−krn⇒U(r)=−∫F(r)dr=−k(n−1)⋅1rn−1 Kinetic energy =L22I=L22mr2=K(r) Since total energy E(r)=U(r)+K(r)⇒E(r)=−k(n−1)⋅1rn−1+L22mr2⇒∂Earr=p=0 and ∂2E∂r2r=D>0, Using both conditions, (3−n)L2m>0