My question is directly, how many elements are in the invertible set $Z_{35}$?
It's my understanding that for any $Z_n$, if $n$ is prime, then the number of invertible elements is equal to $n-1$. In addition, all elements that are invertible satisfy the formula $\gcd(x,n) = 1$. Thus, for $n = 35$, which is composed of two primes, the number of invertible elements should be $n-3$, or $32$. The non-invertible elements namely $0, 5, 7$.
Will someone please show me where I my logic is incorrect. This was a Coursera question that I missed four times, but I can't seem to figure out why unless I am misunderstanding something or missing something very obvious.