MathDB

A set

C

of positive integers is called good if for every integer

k

there exist distinct

a, b \in C

such that the numbers

a+k

and

b+k

are not relatively prime. Prove that if the sum of the elements of a good set

C

equals

2003

, then there exists

c \in C

such that the set

C-\{c\}

is good.

Problem Statement