Question 21
Determine the number of tuples of integers $(a_1, a_2, \dots, a_{17})$ which satisfy $2 \le a_i \le 20$ for all $i = 1, \dots, 17$ and
$$
a_1^{a_2} \cdots a_{16}^{a_{17}} \equiv a_2^{a_3} \cdots a_{17}^{a_{17}} \equiv 1 \pmod{17}.
$$
Here the exponential is calculated in order from upper right two numbers.
$$
a_1^{a_2} \cdots a_{16}^{a_{17}} \equiv a_2^{a_3} \cdots a_{17}^{a_{17}} \equiv 1 \pmod{17}.
$$
Here the exponential is calculated in order from upper right two numbers.