Intereting Posts

Equivalence of the definitions of the Subbasis of a Topology
Is this map to a finite dimensional topological vector space an open map?
Factoring large integers without a cluster
Banach Spaces: Uniform Integral vs. Riemann Integral
Every element in a ring with finitely many ideals is either a unit or a zero divisor.
Finding limit of a quotient with two square roots: $\lim_{t\to 0}\frac{\sqrt{1+t}-\sqrt{1-t}}t$
Solving an integral (with substitution?)
Why is this extension of Galois?
The Strong Whitney Embedding Theorem-Any Recommended Sources?
Showing range is countable
Definition of a Group in Abstract Algebra Texts
Proof of $\frac{1}{e^{\pi}+1}+\frac{3}{e^{3\pi}+1}+\frac{5}{e^{5\pi}+1}+\ldots=\frac{1}{24}$
Evaluating the limit $\lim_{n\to\infty} \left$
Set builder notation, left or right of :| convention
How to integrate $\int_{0}^{\infty }{\frac{\sin x}{\cosh x+\cos x}\cdot \frac{{{x}^{n}}}{n!}\ \text{d}x} $?

Euler and Lamé are said to have proven FLT for $n=3$ that is, they are believed to have shown that $x^3 + y^3 = z^3$ has no nonzero integer solutions. According to Kleiner they approached this by decomposing $x^3 + y^3$ into $(x + y)(x + y\omega)(x + y\omega^2)$ where $\omega$ is the primitive cube root of unity or $w = \frac{-1 + \sqrt{3}i}{2}$.

How would you finish the rest of the proof?

- Given a group $G$, does there exist a domain $D$ with $G$ as its ideal class group?
- The ring of integers of the composite of two fields
- Characterization of finite morsphisms over $\operatorname{Spec }O_K$
- Example of non-trivial number field
- The number of genera of binary quadratic forms of given discriminant
- Showing $\mathbb{Z}+\mathbb{Z}\left$ is a Euclidean domain

- On the origins of the (Weierstrass) Tangent half-angle substitution
- Exact power of $p$ that divides the discriminant of an algebraic number field
- Why are modules called modules?
- The elliptic curve $y^2 = x^3 + 2015x - 2015$ over $\mathbb{Q}$
- Example of non-trivial number field
- Are Primes a Self-Fulfilling Prophecy?
- $I|J \iff I \supseteq J$ using localisation?
- Lack of unique factorization of ideals
- Intuition and Stumbling blocks in proving the finiteness of WC group
- The ring of integers of $\mathbf{Q}$

The proof takes 5 pages in Hardy and Wright, An Introduction to the Theory of Numbers (pages 248 to 253 in the 6th edition). No doubt it can be found in many other intro Number Theory texts, as well as on the web.

Ribenboim’s *Fermat’s Last Theorem for Amateurs* is an excellent resource for this.

You can also check out this blog, but I always found it hard to navigate.

I recommend Harold Edwards’ *Fermat’s Last Theorem.* Euler’s method of infinite descent for the case n = 3 (with a careful explanation of the gap in Euler’s proof) is given and corrected in sections 2.2, 2.5 of this book. This also takes about 5 pages.

This may be the version in Hardy and Wright but I doubt it. Edwards also explains that the idea can be corrected using an idea of Euler’s, so the whole thing is essentially due to Euler.

- How to think deeply in mathematics way?
- Is the $n$-th prime smaller than $n(\log n + \log\log n-1+\frac{\log\log n}{\log n})$?
- holomorphic functions and fixed points
- In a noetherian integral domain every non invertible element is a product of irreducible elements
- Find the volume common to two circular cylinders, each with radius r, if the axes of the cylinders intersect at right angles. (using disk/washer)
- Integral domain with two elements that do not have a gcd
- What is the difference between a complete orthonormal set and an orthonormal basis in a Hilbert space
- Relationship between degrees of continued fractions
- Consider the series $ ∑_{n=1}^∞ x^2+ n/n^2$ . Pick out the true statements:
- How to prove Raabe's Formula
- How to construct a particular convex set (when defining inductive limits of Frechet spaces in Reed and Simon)
- continuous projections to finite dimensional subspaces of normed spaces
- $f_n(x) = x – x^n$ for $x\in $. Does the sequence converge pointwise or uniformly on $$?
- Cohomology groups of a homotopy fiber
- How do I simplify $\sqrt{3}(\cot 70^\circ + 4 \cos 70^\circ )$?