MathDB

Given arbitrary positive integer

a

larger than

1

, show that for any positive integer

n

, there always exists a n-degree integral coefficient polynomial

p(x)

, such that

p(0)

p(1)

\cdots

p(n)

are pairwise distinct positive integers, and all have the form of 2a^k\plus{}3, where

k

is also an integer.

Problem Statement