MathDB

a)

Prove that for all positive integers

n

exists a set

M_n

of positive integers with exactly

n

elements and:

i)

Arithmetic mean of arbitrary non-empty subset of

M_n

is integer

ii)

Geometric mean of arbitrary non-empty subset of

M_n

is integer

iii)

Both arithmetic mean and geometry mean of arbitrary non-empty subset of

M_n

is integer

b)

Does there exist infinite set

M

of positive integers such that arithmetic mean of arbitrary non-empty subset of

M

is integer

Problem Statement