EN
Let k be a field. We describe all linear derivations d of the polynomial algebra k[x₁,...,xₘ] such that the algebra of constants with respect to d is generated by linear forms: (a) over k in the case of char k = 0, (b) over $k[x₁^{p},...,xₘ^{p}]$ in the case of char k = p > 0.