Збережено в:
| Автор: | |
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| Формат: | Recurso digital |
| Мова: | |
| Опубліковано: |
Zenodo
2026
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| Онлайн доступ: | https://doi.org/10.5281/zenodo.19903519 |
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Зміст:
- <p>We establish a complete criterion for the solvability by radicals of</p> <p>algebraic equations in standard form, where non-zero terms are spec-</p> <p>ified by a set of indices M ⊆ {1, 2, . . . , n} with arbitrary complex</p> <p>coefficients. The criterion is based on the residue classes of indices</p> <p>modulo 4, termed channels. We prove that an equation in standard</p> <p>form is solvable by radicals if and only if it satisfies the channel pri-</p> <p>ority rule: when indices from multiple channels are present, only the</p> <p>smallest index (i.e., the term of highest degree) may be retained from</p> <p>each channel; when only a single channel is used, any index within that</p> <p>channel is permitted. The proof reduces the problem to equations of</p> <p>degree at most 4, which are classically solvable.</p>