Problem

Source: Oliforum Contest V 2017 p3 https://artofproblemsolving.com/community/c2487525_oliforum_contes

Tags: number theory, Product, primes



Do there exist (not necessarily distinct) primes $p_1,..., p_k$ and $q_1,...,q_n$ such that $$p_1! \cdot \cdot \cdot p_k! \cdot 2017 = q_1! \cdot \cdot \cdot q_n! \cdot 2016 \,\,?$$ (Paolo Leonetti)