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I need a little help. I am looking for answers to these questions.

1) Can you give me a direct PDF resource for read Abel's impossibility theorem (not Abel-Ruffini theorem) ? I can not find. In Wolfram Mathworld I found only this information:

" In general, polynomial equations higher than fourth degree are incapable of algebraic solution in terms of a finite number of additions, subtractions, multiplications, divisions, and root extractions. This was also shown by Ruffini in 1813 (Wells 1986, p. 59) ".

2) What is the difference between Abel's theorem and Abel Ruffini's theorem?

3) Is the method used in Abel's theorem completely algebraic? Do I need to have strong high math knowledge to understand the theorem?

P.S. Maybe everybody knows the answer to these questions. Since I have not a math teacher, I had to ask these questions in MSE. I may not have picked the tags correctly.

Thank you.

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  • $\begingroup$ For me Abel-Ruffini for me is the same as Abel's impossibility theorem (and so is it for wikipedia). The proof relies on Galois theory and can also be found on the wikipedia page $\endgroup$ Jun 21, 2018 at 10:13
  • $\begingroup$ Yes, I'm confused, too. Why do you think they are any different? $\endgroup$
    – tomasz
    Jun 21, 2018 at 10:14
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    $\begingroup$ @tomasz names are different, I thought so. Because I do not know about the content .. $\endgroup$ Jun 21, 2018 at 10:17
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    $\begingroup$ @Student: it's really not that uncommon for a concept to have two different names. If you look at the statement of the "impossibility theorem" on Wolfram and the "Abel-Ruffini theorem" on Wikipedia, they are the same. $\endgroup$
    – tomasz
    Jun 21, 2018 at 11:26

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You have already been told in the comments that the Abel-Ruffini theorem and Abel's impossibility thorem are the same thing. Concerning the proof of the theorem, it is purely algebraic and it doesn't require deep algebra. Of course, it does not use Galois theory, since it had not yet been created. I suggest that you read these articles:

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