Let $\lambda_n=1-1/n$ for $n=1,2,\dots.$ Show that there cannot be a regular or periodic Sturm-Liouville problem having these numbers as eigenvalues.

Question

How does one show that this is true? I assume it has to do with the properties of the y solutions since they are either $y(x)=c_1e^{kx}+c_2e^{-kx}$, where $\lambda=-k^2, k<0$; or $y(x)=c_1\cos(kx)+c_2\sin(kx)$ where $\lambda=k^2, k>0.$