Which of the following CANNOT be a product of two distinct positive integers a and b?  Choose the most appropriate option:
A) a B) b C) 3b + 2a D) b - a E) ba
we can eliminate answer choices A, B, and E right away. There is no reason to distinguish between aa and bb, so if aa cannot be a product, then bb cannot be either and since we cannot have two correct answers in PS problems, then neither A nor B can be correct. As for E it's clearly cannot be correct answer.   So, we are left with options C and D.   For C, can ab=3b+2aab=3b+2a? --&gt; ab−2a=3bab−2a=3b --&gt; a(b−2)=3ba(b−2)=3b --&gt; a=3bb−2a=3bb−2. Now, if b=3b=3, then a=9a=9, so in this case ab=3b+2aab=3b+2a is possible.   Only option left is D.   Answer: b - a.
<result>D</result>
Which of the following CANNOT be a product of two distinct positive integers a and b?