Fermat's Last Theorem

The purpose of this blog is to present the story behind Fermat's Last Theorem and Wiles' proof in a way accessible to the mathematical amateur.

Saturday, August 05, 2006

Ideal Numbers: Prime Cyclotomic Integers

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The beauty of Ernst Kummer's prime divisors is that they have the same "action" as the real cyclotomic primes when they exi...
Friday, August 04, 2006

Ideal Numbers: Additive Group of Cyclotomic Integers Mod p

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In today's blog, I will introduce the idea of Additive Groups and talk specifically about the Additive Group of Cyclotomic Integers Mod ...
Wednesday, August 02, 2006

Ideal Numbers: Cyclotomic primes that divide a prime p ≠ λ

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In a previous blog , I spoke about the properties of α - 1 and I showed that α - 1 is the only cyclotomic prime that divides λ . In today...

Ideal Numbers: α - 1

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From the perspective of ideal numbers , there are two types of prime divisors. Prime divisors that divide a prime integer p where p ≠ λ (...
Tuesday, July 25, 2006

Cyclotomic Integers: Periods mod p

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Today's blog continues the details that are used by Ernst Kummer in his theory of ideal numbers . He then uses ideal numbers in his pr...

Cyclotomic Integers: Unique Factorization Fails

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Unique factorization fails for cyclotomic integers starting with λ = 23 where λ represent the primitive root of unity that a given cycloto...
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