Problem Solving (PS) | How many different pairs of integers (a, b) exist such that 2

Here is my take.

I first started with non-negative integers. For example, I tried forming the inequality using the integer 2 first. I realized that there were 2 cases, when a=2 and b=0. The other case is when a=2 and b= 1. So we have two cases for the integer 2. Then I moved to the integer 3, here as well you will find two cases- one in which a=3 and b=0 and the other in which a-3 and b=1. On further speculation you will realize that there are 2 possible cases for each of the values of a from
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