QuestionFor a prime number $w > 2$ , when is $w^{2} z$ a negative even integer for $z$ in which set? A. Negative integers B. Positive odd integers C. Positive even integers D. Negative odd integers E. Negative even integers

Studdy Solution

STEP 1

Assumptions1. $w$ is a positive prime number greater than. $w^{} z$ is always a negative even integer3. $z$ is an integer

STEP 2

We know that $w$ is a positive prime number greater than2. This means $w$ is an odd number because the only even prime number is2. Therefore, $w^2$ is also an odd number because the square of an odd number is always odd.

STEP 3

We want $w^{2} z$ to be a negative even integer. Since $w^{2}$ is odd, we need $z$ to be negative and even because the product of an odd number and an even number is always even.

STEP 4

So, the set of integers that $z$ can be is the set of all negative even integers.
Therefore, the answer is. The set of all negative even integers.

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