hi every one
can any buby help me with these questions?

1. If a,b are in N*, if gratest common div.(a,b) & smallest com. mult.(a,b) are squares, show that a,b are squares.

2. Show that for every m>0 , a?1 we have

( a^m -1 / a-1 , a-1 ) = ( a-1 , m ).

3. show that any two terms in the sequance: 2+1, 2^2+1, 2^4+1, .. , 2^2n+1 are coprime .