Strong-pseudoprime bases for a product of two primes with common predecessor divisor ten

Let $N=pq$ for distinct odd prime numbers $p,q$ with $\gcd (p-1,q-1)=10$. Exactly $100$ unit bases make $N$ a Fermat pseudoprime, and exactly $50$ of these make it a strong pseudoprime. The Fermat bases form $C_{10}\times C_{10}$ under the Chinese remainder theorem for unit groups. If $N-1=2^{s}m$, then $5\mid m$ and $m$ is odd, so the $m$th-power map sends five elements of each $C_{10}$ to $1$ and five to $-1$. The strong condition requires equal signs in both components, giving $5^2+5^2=50$.