# Tag Info

### Almost Pell type equation

If you multiply this by $2$ you get $(2x)^2 - 2N y^2 = -2$, so you can solve $x^2 - 2N y^2 = -2$ and then check when $x$ is even. $x^2 - 2Ny^2 = -2$ is a generalized Pell's equation, so you can find a ...
Accepted

### Representation of a number as a product of $\sqrt{n^2 + 1} + n$

$\def\supp{\mathop{\mathrm{supp}}}$ Surely, in the Almost equivalent question'' you assume that the $d$'s are square-free. Denote $R=\mathbb Z[\sqrt{p_1},\dots,\sqrt{p_n}]$. We prove that in its ...
• 21.3k

### Representing $x^6-4$ as a sum of two squares

This problem looks tricky. I'd recommend you look up "Châtelet surfaces"; these are a slightly easier case when one has a polynomial of degree $4$ instead of a polynomial of degree $6$, but ...
• 20.1k
### Representing $x^3-2$ as a sum of two squares
One more way to solve the problem. Let $x = 4t + 3$. Then $$x^3 - 2 = 16t^2(4t + 9) + (108t + 25).$$ The system $$4t + 9 = a^2 \qquad 108t + 25 = b^2$$ has infinitely many solutions. It is reduced to ...