In this article, we give some comments on the article 'Numerical approach to the non-linear diofantic equations with applications to the controllability of infinite dimensional dynamical systems'. The article gives an algorithm for the controllability analysis of the parabolic dynamical system defined in the n-D rectangular prism. The severe drawback of that algorithm is multiple nested, time-consuming loops which are necessary to perform. In the comments, we propose how to avoid performing sophisticated algorithms in that problem thanks to involving new advanced results of the number theory.