Math Help - Fermat pseudoprime

1. Fermat pseudoprime

2. For the 1st one, its easy to see that $91 = 7 * 13$ so its definitely not prime.

Also $3^{90} = 1mod\ 90$ (from observation)

You can also construct a new pseudoprime N using the proposition:

Let b >= 2 (where b is the base of this pseudoprime) and p an odd prime where p does not divide b(b-1)(b+1) then

$N = \frac{b^p -1}{b-1}*\frac{b^p+1}{b+1}$

If someone could review this and check for correctness, that would be great!
Edit: it works fine.