MathDB

Let

n

and

k

be integers,

1\le k\le n

. Find an integer

b

and a set

A

n

integers satisfying the following conditions: (i) No product of

k-1

distinct elements of

A

is divisible by

b

. (ii) Every product of

k

distinct elements of

A

is divisible by

b

. (iii) For all distinct

a,a'

A

a

does not divide

a'

Problem Statement