I was reading a paper by A.L. Whitman on Family of Difference Sets, on page 109, the author generalizes the reduced residue system modulo $v$ where $v=pq$, $p$ and $q$ are primes. At the last paragraph can someone explain if $p-1=df$ and $q-1=ef'$ and $(f,f')=1$, if $ff'$ is odd, then $-1 \equiv g^{(d/2)}(mod\: v)$ and if $ff'$ is even, there does not any such $s (s=0,\ldots, d-1)$ where $d$ is $lcm(p-1.q-1)$ such that $-1 \equiv g^{s}(mod\: v)$.