 There is a number \(n\) such that \(\phi_n(x) = x + n\). (This follows by taking \(f(x,y) = x + n\) in  Corollary 3.2.  Analogous observations yield the existence of \(n\) such that \(\phi_n(x) = x \times n, \phi_n(x) = x^n\), etc.)