On Primality Tests for Mersenne and Fermat Numbers
碩士 === 輔仁大學 === 數學系碩士班 === 106 === Abstract In this master thesis, we will briefly introduce some well-known results on Mersenne and Fermat numbers in Chapter 1. In Section 1.3, we will also introduce the Lucas-Lehmer sequences and outline their useful corresponding properties with complete proo...
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| Format: | Others |
| Language: | en_US |
| Published: |
2018
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| Online Access: | http://ndltd.ncl.edu.tw/handle/748nva |
| Summary: | 碩士 === 輔仁大學 === 數學系碩士班 === 106 === Abstract
In this master thesis, we will briefly introduce some well-known results on Mersenne and Fermat numbers in Chapter 1. In Section 1.3, we will also introduce the Lucas-Lehmer sequences and outline their useful corresponding properties with complete proofs.
In Chapter 2, we will study the Lucas-Lehmer primality test for Mersenne numbers. And in Chapter 3, we will study the Pepin{'}s primality test for Fermat numbers. Via Lucas-Lehmer sequences, both tests share a common nature. We will outline these ideas with complete discussions here.
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