Fermat's Last Theorem

In my last blog , I spoke about the importance of unique factorization of integers . This is the idea that all integers can be broken up int...

Carl Friedrich Gauss was the first mathematician to understand the importance of unique factorization in relation to algebraic integers. W...

Carl Friedrich Gauss was born on April 17, 1777 to poor, working class parents in Brauschweig, Germany. His mother had been a maid and his f...

For those who are not familiar with Fermat's Last Theorem , you may wish to start here . In Leonhard Euler's original proof for Fer...

It may surprising that we only need one more lemma to finish Euler's proof for Fermat's Last Theorem: n=3. This is an easy one. For...

Today's blog is a bit shorter than the previous ones. It shows the relationship which was probably the original reason why Pierre de Fer...

In today's blog, I will go over the case of where a 2 + 3b 2 is an even number. This result is part of the proof of Fermat's Last ...

In today's blog, I will show that if you divide a polyonomial of form a 2 + 3b 2 with a prime of this same form, then you end up a pol...

Today's blog presents another lemma associated with the polynomial a 2 + 3b 2 . This lemma is used in the proof for Fermat's Last T...

The essence of Euler's proof for Fermat's Last Theorem, n = 3 , is realizing the properties of values that can be represented by th...

One of the surprising discoveries in the Fermat's Last Theorem n=3 is how much more complicated it is than n=4 . In this blog, I will p...

Today's blog continues the proof for Fermat's Last Theorem n=3 which was started in a previous blog . Lemma: Given the following co...

Today's blog continues the proof for Fermat's Last Theorem n=3 that I began in a previous blog . With this step, we enter the heart...

Today's blog continues the proof that I started earlier. The full proof for Fermat's Last Theorem: n = 3 can be found in my previou...

This blog will explain the proof for the first step in Fermat's Last Theorem: n = 3 . For the full proof, please start here . The detail...

Leonhard Euler came up with two proofs for Fermat's Last Theorem : n = 3. One proof involved a very innovative method using irrational ...

The next mathematician in the story of Fermat's Last Theorem is Leonhard Euler , whose name is pronounced "Oiler". Euler was ...

The easiest proof for Fermat's Last Theorem is the case n = 4 . The proof for n=3 is a bit tricker. What is nice about this proof ...

In his life, Pierre de Fermat only left one proof in relation to number theory . He used his method of infinite descent to show that the a...