New posts in Diophantine Equations

triangles in $\mathbb{R}^n$ with all vertices in $\mathbb{Q}^n$

$x^2-(p^4-16)y^2=p^2 \land x \mod (p^2-4) =2 \land x >0 \implies p | x,y$?

Integer solutions of $3^n-1=2m^2$

A System of Simultaneous Pell Equations

The Diophantine equation $x_1^6+x_2^6+x_3^6=z^2$ where exactly one $(x_i)\equiv 0{\pmod 7}$.

The Proof of Infinitude of Pythagorean Triples $(x,x+1,z)$

Prove that the number of answers for $|a_1|+|a_2|+...+|a_k| \le n$ is equal to the number of answers for $|a_1|+|a_2|+...+|a_n| \le k$.

A Diophantine equation solved when N is not a square?

What are the units in $\mathbb{Q}(\sqrt{2}, \sqrt{3})$?

Can a parallelogram have whole-number lengths for all four sides and both diagonals?