For how many positive integers n is
an integer ?
If n is a positive even integer,, which is not divisible by .
Now suppose n is a positive odd integer.
When. , which is divisible by 2, 8 and 32, but not by 128.
Supposeis divisible by by 2, 8 and 32 but not by 128 for some odd integer n.
Thenis also divisible by 2, 8 and 32 but not by 128.
Hence, by induction,is divisible by 2, 8 and 32 but not by 128 for all positive odd integers n.
So there are only three positive integers n (namely) for which
is an integer.