Find all elements in <Z/90Z,+> that generate the whole group.

My solution:

a in {0,1,...,89} generates the given group iff gcd (a,90)=1 iff a exists in {1,7,11,13,17,19,23,29,31,37,41,43,47,49,53,59,61, 67,71,73,77,79,83,89}

Can someone please review my solution and confirm it? Thanks in advance!