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The question in question asks whether the AM-GM inequality can be, in some sense, reduced to the case where there is equality. I think this is a reasonable question, and here is a proposed plan for an answer: one could outline a proof for the inequality, in which one brings two variables together, and shows that this decreases the GM without changing the AM; after finitely many such operations, we are left with the case of equality.

The OP also recently asked another contentious question, which doesn't make much sense to me, and was promptly closed. A possible different course of action, which might be less alienating, is to ask the OP to explain his motives better.

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    $\begingroup$ don't accept the answer yet. I think questions with no accepted answers tend to get more views. :) And it is better to click the green check mark after either (a) question is re-opened or (b) the community decides it shouldn't be re-opened. $\endgroup$ – Willie Wong Apr 30 '11 at 0:42
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First, I just want to note that the second question about $\pi(x)$ is not in fact promptly closed. As of the writing of this answer there are some close votes on it, but it is still open.

For the first question, I had to look up what codicil means in the dictionary. And even after looking it up, I still don't think I understand what the question actually means. On the other hand, your description sounds like a reasonable question. If you edit the question into a way that I understand better, I would voice my support (unfortunately my re-open vote would be also binding, just like my close votes) for a question about "whether the AM-GM inequality can be reduced to the case of the equality".

(Mathematically, I think the answer is yes. But I don't think it is a hundred times easier to prove the AM-GM inequality that way...)

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