1. This is a result of Galois theory (see Quintic equations and the Abel–Ruffini theorem).

2. The truth and importance of the work were not confirmed during his lifetime. His work laid the fundamental foundations for Galois theory , a major branch of abstract algebra and of pseudorandom sequence (PN) and error-correction coding applications.

3. This line of work ultimately resulted, through the work of Évariste Galois, in Galois theory, which gives a complete description of what is possible and impossible with respect to solving polynomial equations (in one unknown) by radicals.

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