TAOCP 3.2.1.3 Exercise 2
In the MIX code (3) we have $a = B^2 + 1$, so $b = a - 1 = B^2$.
Exercise 2. [10] What is the potency of the generator represented by the MIX code (3)?
Verified: yes
Solve time: 1m08s
In the MIX code (3) we have $a = B^2 + 1$, so $b = a - 1 = B^2$. The modulus is $m = B^5$, and we seek the least integer $s$ such that $b^s \equiv 0 \pmod{m}$. We have
$b^1 = B^2 \not\equiv 0 \pmod{B^5}, \qquad b^2 = B^4 \not\equiv 0 \pmod{B^5}, \qquad b^3 = B^6 \equiv 0 \pmod{B^5}.$
Hence the potency of the generator is $s = 3$, since $B^6$ is the first power of $b$ divisible by $m$.
$$ \boxed{3} $$