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I have a need to modify Erdős' proof of the Sylvester-Schur Theorem to prove something stronger. See my working document at http://math.rudytoody.us/ or http://math.rudytoody.us/OppermannTheorem.pdf

If I have to modify most of the proof, I will use the entire proof (with proper attribution, of course.) However, I don't believe I will need to do that. So, how much should I show of the original? Could I do a line-by-line comparison of the changes? If I only change a few variables, could I do something along the lines of, "By changing variables a, b, c and relaxing condition x, it's easy to see that Erdős' proof arrives at the same conclusion without breaking the original."

Some suggestions would be appreciated. Thanks.

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    $\begingroup$ Short answer: "It depends on who your audience is, and what they might expect of you" $\endgroup$
    – Yemon Choi
    Commented Aug 16, 2011 at 1:06
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    $\begingroup$ Most people in this audience to not have the Erdös paper handy, so probably your including a complete proof would be best. $\endgroup$ Commented Aug 16, 2011 at 1:34
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    $\begingroup$ Heck, I didn't even know what the Sylvester-Schur theorem (see math.uiuc.edu/~pppollac/sschur.pdf) was. My guess is that most people won't know the theorem. So I'd agree with Gerald Edgar: if it's this audience, you should provide a complete statement and proof. You can then comment on how the proof compares to that of Erdös if you like, or say that it is patterned after that of Erdös, or whatever. BTW: I didn't feel like copying and entering your link into my browser -- laziness. Why don't you provide a direct link? $\endgroup$
    – Todd Trimble
    Commented Aug 16, 2011 at 1:59
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    $\begingroup$ Erring on the side of caution is best here: you can always write out the whole proof; if an editor or referee feels it's unnecessary, they will probably point it out. $\endgroup$ Commented Aug 16, 2011 at 2:09
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    $\begingroup$ I suggest you write your own proof completely, then mention that your proof is a modification of the proof of Erdös, then cite his paper. $\endgroup$
    – JRN
    Commented Aug 16, 2011 at 2:47

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I'm following Todd Trimble's suggestion and writing my comment as an answer:

I suggest you write your own proof completely, then mention that your proof is a modification of the proof of Erdős, then cite his paper.

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