Are there prime numbers n for which S=/0?

[koulis]

We have the set:S={1<a<n:gcd(a,n)=1,a^(n-1)=/1(modn)}
Are there prime numbers n for which S=/0?After this, are there any composite numbers n for which S=0?

(with =/ i mean the 'not equal' and '0' is the empty set)

for the first one i know that there are no n prime numbers suh that S to be not empty from Fermat's little theorem.Any ideas or hints for the second one?

 

[Dick]

We have the set:S={1<a<n:gcd(a,n)=1,a^(n-1)=/1(modn)}
Are there prime numbers n for which S=/0?After this, are there any composite numbers n for which S=0?

(with =/ i mean the 'not equal' and '0' is the empty set)

for the first one i know that there are no n prime numbers suh that S to be not empty from Fermat's little theorem.Any ideas or hints for the second one?

Try it for a few small composite values of n. And be careful, 2 is prime.