All Questions

As many of you may know, the illustrious L. Euler put forward a proof of the case $n=3$ of Fermat's Last Theorem via infinite descent. The thing is that, at a certain point, he resorted to the ...

Let $\mathbb{Q}^{\text{ab}}$ be the compositum of all finite abelian extensions of $\mathbb{Q}$. Explicitly, $\mathbb{Q}^{\text{ab}}$ is the field obtained from $\mathbb{Q}$ by adjoining all roots of ...

I am studying diophantine equations and I need the theory of Bakers, Can you advise me about good books, or lectures on Baker's theory?

Many modern proofs of the (ineffective) finiteness of solutions of the $S$-unit equation $x+y=1$ use Roth's theorem. In particular it is used Lang's version of Roth's theorem which takes in account ...

The open problem of magic squares of squares explained here. Consider the following magic square of squares: $$ \begin{aligned} &a^2&b^2&&c^2\\\\ &d^2&e^2&&f^2\\\\ &...

Let $N$ be a fixed positive integer that is not a square and $m$ be any nonzero integer. Let $x$ and $y$ be positive integers that solve $$x^2 - N y^2 = m^2$$ with $x + y$ minimal (in light of the ...