Niven’s Theorem
| Autor: | Adam Naumowicz, Artur Korniłowicz |
|---|---|
| Jazyk: | angličtina |
| Rok vydání: | 2016 |
| Předmět: |
Discrete mathematics
niven’s theorem Factor theorem 12d10 Proofs of Fermat's little theorem Fundamental theorem Applied Mathematics 010102 general mathematics 01 natural sciences Squeeze theorem integral root theorem Bruck–Ryser–Chowla theorem Computational Mathematics 97g60 Niven's theorem 03b35 QA1-939 0101 mathematics rational root theorem Brouwer fixed-point theorem Mathematics Carlson's theorem |
| Zdroj: | Formalized Mathematics, Vol 24, Iss 4, Pp 301-308 (2016) |
| ISSN: | 1898-9934 1426-2630 |
| Popis: | Summary This article formalizes the proof of Niven’s theorem [12] which states that if x/π and sin(x) are both rational, then the sine takes values 0, ±1/2, and ±1. The main part of the formalization follows the informal proof presented at Pr∞fWiki (https://proofwiki.org/wiki/Niven’s_Theorem#Source_of_Name). For this proof, we have also formalized the rational and integral root theorems setting constraints on solutions of polynomial equations with integer coefficients [8, 9]. |
| Databáze: | OpenAIRE |
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