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Formalized Mathematics

(a computer assisted approach)

Editor-in-Chief: Matuszewski, Roman

4 Issues per year


SCImago Journal Rank (SJR) 2016: 0.207
Source Normalized Impact per Paper (SNIP) 2016: 0.315

Open Access
Online
ISSN
1898-9934
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Volume 24, Issue 4 (Dec 2016)

Issues

Niven’s Theorem

Artur Korniłowicz / Adam Naumowicz
Published Online: 2017-02-23 | DOI: https://doi.org/10.1515/forma-2016-0026

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].

Keywords: Niven’s theorem; rational root theorem; integral root theorem

MSC 2010: 97G60; 12D10; 03B35

References

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About the article

Received: 2016-12-15

Published Online: 2017-02-23

Published in Print: 2016-12-01


Citation Information: Formalized Mathematics, ISSN (Online) 1898-9934, ISSN (Print) 1426-2630, DOI: https://doi.org/10.1515/forma-2016-0026.

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© 2016 Artur Korniłowicz et al., published by De Gruyter Open. This work is licensed under version 3.0 of the Creative Commons Attribution–ShareAlike License. BY-SA 3.0

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