Let a~[0], ... , a~[n] be real numbers such that a~[0] is nonzero, and let L be the following linear operator: a~[n]D^n + ... + a~[1]D + a~[0]I.

Let p(t) be a polynomial. Let us define the functions y~[0] = p(t). and: y~[k+1] = p(t) - (a~[n]D^n + ... + a~[1]D)[y~[k]].

Prove that the functions y~[k](t) converge to a polynomial y(t), and that L[y] = p(t)