Hi everybody!

I have been working on the following number problem for half a year, but still unable to figure it out. Could someone help me?

PROBLEM: Given n elements a[1], a[2] ... a[n], let A be a set such that:

1. All element a[1], a[2] ... a[n] belong to A.

2. If x, y belong to A, GCD(x, y) and LCM(x, y) belong to A.

Task: Given a number x, determine if x belongs to A.

Thank you.