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I am currently reading a paper which treats Abel’s original proof of Ruffini-Abelian theorem but I got stuck on a theorem at the beginning of the paper.

Theorem 1 in the paper

I understand the argument prior to theorem 1, but I don’t understand why the argument just before theorem 1 indeed proves it.

The link of the original paper:

On the Ruffini-Abelian Theorem

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