MathDB

k

and

n

are positive integers that are greater than

1

N

is the set of positive integers.

A_1, A_2, \cdots A_k

are pairwise not-intersecting subsets of

N

and

A_1 \cup A_2 \cup \cdots \cup A_k = N

. Prove that for some

i \in \{ 1,2,\cdots,k \}

, there exsits infinity many non-factorable n-th degree polynomials so that coefficients of one polynomial are pairwise distinct and all the coeficients are in

A_i

Problem Statement