On the coincidence of the class of bent-functions with the class of functions which are minimally close to linear functions

For functions from $(\mathbb Z/(p))^n$ to $(\mathbb Z/(p))^m$ where $p$ is a prime, the property of closeness to linear functions is investigated. It is proved that, for any function, this property is inherited by its homomorphic images. As a generalization of an analogous statement for Boolean functions it is shown that if $p=2$ or $3$ then the class of functions which are absolutely minimally close to linear ones coincides with the class of bent-functions.