Problem 4

Part of 1990 Bulgaria National Olympiad

Problems(1)

NT set, x+y in M implies x or y in M

Source: Bulgaria 1990 P4

M

is an infinite set of natural numbers such that, whenever the sum of two natural numbers is in

M

, one of these two numbers is in

M

as well. Prove that the elements of any finite set of natural numbers not belonging to

M

have a common divisor greater than

1

number theorysetSets