4 problems

Tunnell's conjecture. The integer $n$ is a congruent number if and only if

Let $n$ be a positive integer power of $2$, so that $n\in 2^{\mathbb{N}}$. A positive integer is congruent if it is the area of a right triangle with rational side lengths. Noncong…

Unique hypotenuse multiplicity conjecture. There do not exist two dissimilar primitive right triangles with the same hypotenuse and whose squarefree parts of the areas are equal to…

Congruent number conjecture for angles $\pi/3$ and $2\pi/3$. If