Question 20
Do there exist positive integers $a_1, a_2, \dots, a_{2017}$ such that the product
$$
(a_1^{2017} + a_2)(a_2^{2017} + a_3) \dots (a_{2016}^{2017} + a_{2017})(a_{2017}^{2017} + a_1)
$$
is a power of a prime with exponent
a) $2017 \cdot 2018,$
b) $2017 \cdot 2023.$
$$
(a_1^{2017} + a_2)(a_2^{2017} + a_3) \dots (a_{2016}^{2017} + a_{2017})(a_{2017}^{2017} + a_1)
$$
is a power of a prime with exponent
a) $2017 \cdot 2018,$
b) $2017 \cdot 2023.$