Question 183
a) Determine whether there exist positive integers $a_1, a_2, \ldots, a_{2015}$ such that any two of them are coprime and $a_1a_2\ldots a_{2015}-1$ is a product of two consecutive odd numbers.
b) Determine whether there exist positive integers $a_1, a_2, \ldots, a_{2015}$ such that any two of them are coprime and $a_1a_2\ldots a_{2015}-1$ is a product of two consecutive even numbers.
b) Determine whether there exist positive integers $a_1, a_2, \ldots, a_{2015}$ such that any two of them are coprime and $a_1a_2\ldots a_{2015}-1$ is a product of two consecutive even numbers.