A Note on LSI polynomials and Comments on a 'Proof of a Modified form of Shanks' Conjecture'

Least Square Inverse (LSI) polynomials are classified into optimal and suboptimal LSI polynomials and the stability of LSI polynomials are investigated in the light of this classification. It is shown that a recent proof of the modified form of Shanks' conjecture is based on the stability of 1-D suboptimal LSI polynomials which is not guaranteed. This invalidates the proof and leaves the modified Shanks' conjecture yet to be proved.