Question 56
Find the number of ordered 6-tuples satisfying the following system of modular equations
$$
\begin{cases}
ab + a'b' \equiv 1 \pmod{15} \\
bc + b'c' \equiv 1 \pmod{15} \\
ca + c'a' \equiv 1 \pmod{15}
\end{cases}
$$
with $a, b, c, a', b', c' \in \{0, 1, \dots, 14\}$.
$$
\begin{cases}
ab + a'b' \equiv 1 \pmod{15} \\
bc + b'c' \equiv 1 \pmod{15} \\
ca + c'a' \equiv 1 \pmod{15}
\end{cases}
$$
with $a, b, c, a', b', c' \in \{0, 1, \dots, 14\}$.