MathDB

A subset

A

of the natural numbers

\mathbb{N} = \{0, 1, 2,\dots\}

is called good if every integer

n>0

has at most one prime divisor

p

such that

n-p\in A

. (a) Show that the set

S = \{0, 1, 4, 9,\dots\}

of perfect squares is good. (b) Find an infinite good set disjoint from

S

. (Two sets are disjoint if they have no common elements.)

Problem Statement