TITLE: What is the protocol for making modifications to someone else's proof to prove something slightly stronger?
QUESTION [12 upvotes]: 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.

REPLY [15 votes]: 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.