Intereting Posts

Are there necessary and sufficient conditions for Krein-Milman type conclusions?
What makes elementary functions elementary?
Description of the kernel of the tensor product of two linear maps
Example of $f,g: \to$ and riemann-integrable, but $g\circ f$ is not?
Reference for combinatorial game theory.
Numbers which are not the sum of distinct squares
Given $f, g \in k$ coprime, why can we find $u,v \in k$ such that $uf + vg \in k\setminus\{0\}$?
Two exercises on characters on Marcus (Part 2)
Examples of mathematical results discovered “late”
Evaluate $\int\frac{d\theta}{1+x\sin^2(\theta)}$
Appearance of Formal Derivative in Algebra
Norm of powers of a maximal ideal (in residually finite rings)
What's the idea behind the Taylor series?
$\int_{1}^{\infty} h(x)\ dx$ converges $\Rightarrow$ $h$ is bounded in $[1, \infty)$
Union of two vector subspaces not a subspace?

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?

- Significance of the Riemann hypothesis to algebraic number theory?
- For which values of $d<0$ , is the subring of quadratic integers of $\mathbb Q$ is a PID?
- Proving that $\cos(2\pi/n)$ is algebraic
- An element is integral iff its minimal polynomial has integral coefficients.
- Euclidean domain $\mathbb{Z}$
- Ideal generated by 3 and $1+\sqrt{-5}$ is not a principal ideal in the ring $\Bbb Z$

- On the absolute norm of an ideal
- The form $xy+5=a(x+y)$ and its solutions with $x,y$ prime
- Is the theory of dual numbers strong enough to develop real analysis, and does it resemble Newton's historical method for doing calculus?
- Book(s) Request to Prepare for Algebraic Number Theory
- Who realized $\int \frac 1x dx =\ln(x)+c$?
- Class group and factorizations
- Intuition regarding Chevalley-Warning Theorem
- Ring class field of $\mathbb{Q}(\sqrt{-19})$
- Decomposition of a prime number in a cyclotomic field
- Determining ring of integers for $\mathbb{Q}$

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.

- Conditions for vectors to span a vector space
- Integral around unit sphere of inner product
- Eigenvalue and Eigenvector for the change of Basis Matrix
- $\int_0^1 x^n \log^m (1-x) \, {\rm d}x$
- If $G$ has only one subgroup of order $n$, then that Subgroup is Normal
- Degree of a field extension when compared to the Galois group
- Dice Roll Cumulative Sum
- Proving no polynomial $P(x)$ exists such that $P(a) = b$, $P(b) = c$, $P(c) = a$
- How many digits of $\pi$ are currently known?
- Show that any set in a metric space can be written as the intersection of open sets
- Is a direct limit of topological groups always a topological group?
- Derive quadratic formula
- Statistics: Finding posterior distribution given prior distribution & R.Vs distribution
- references for the spectral theorem
- Finding all reals such that two field extensions are equal.