How many integer solutions are there for x + y + z + w = 15 if x ≥ 3,y > −2, z ≥ 1, w > −3?

Question

How many integer solutions are there for x + y + z + w = 15 if x ≥ 3,y > −2, z ≥ 1, w > −3?
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Solution 1

To solve this problem, we can use the method of generating functions or the stars and bars method. However, the stars and bars method is more straightforward in this case. Here are the steps:

  1. Adjust the variables to meet the constraints:
    • Since x ≥ 3, let x = x' + 3. Then x' ≥ 0.
    • Since Knowee AI StudyGPT is a powerful AI-powered study tool designed to help you to solve study prob
Knowee AI StudyGPT is a powerful AI-powered study tool designed to help you to solve study problem.
Knowee AI StudyGPT is a powerful AI-powered study tool designed to help you to solve study problem.
Knowee AI StudyGPT is a powerful AI-powered study tool designed to help you to solve study problem.
Knowee AI StudyGPT is a powerful AI-powered study tool designed to help you to solv

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