MathDB

P(x)

is a monoic polynomial with integer coefficients so that there exists monoic integer coefficients polynomials

p_1(x),p_2(x),\dots ,p_n(x)

so that for any natural number

x

there exist an index

j

and a natural number

y

so that

p_j(y)=P(x)

and also

deg(p_j) \ge deg(P)

for all

j

.Show that there exist an index

i

and an integer

k

so that

P(x)=p_i(x+k)

Problem Statement