Solve a problem of your own!
Download the Studdy App!

Math

Math Snap

PROBLEM

For a prime number w>2w > 2, when is w2zw^{2} z a negative even integer for zz in which set? A. Negative integers B. Positive odd integers C. Positive even integers D. Negative odd integers E. Negative even integers

STEP 1

Assumptions1. ww is a positive prime number greater than. wzw^{} z is always a negative even integer3. zz is an integer

STEP 2

We know that ww is a positive prime number greater than2. This means ww is an odd number because the only even prime number is2. Therefore, w2w^2 is also an odd number because the square of an odd number is always odd.

STEP 3

We want w2zw^{2} z to be a negative even integer. Since w2w^{2} is odd, we need zz to be negative and even because the product of an odd number and an even number is always even.

SOLUTION

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

Was this helpful?
banner

Start understanding anything

Get started now for free.

OverviewParentsContactPolicyTerms
TwitterInstagramFacebookTikTokDiscord