MathDB

Given a non-zero integer

y

and a positive integer

n

. If

x_1, x_2, \ldots, x_n \in \mathbb{Z} - \{0, 1\}

and

z \in \mathbb{Z}^+

satisfy

(x_1x_2 \ldots x_n)^2y \le 2^{2(n+1)}

and

x_1x_2 \ldots x_ny = z + 1

, prove that there is a prime among

x_1, x_2, \ldots, x_n, z

.
It appears that the problem statement is incorrect; suppose

y = 5, n = 2

, then

x_1 = x_2 = -1

and

z = 4

. They all satisfy the problem's conditions, but none of

x_1, x_2, z

is a prime. What should the problem be, or did I misinterpret the problem badly?

Problem Statement