So there is this question our professor gave us at the end of the lecture to think about and it goes:
Prove that $n$ is $t-$congruent iff the following:
i) Either both $\frac{n}{t}$ and $t^2+1$ are non zero rational squares.
ii) or the Elliptic curv: $C_{n,t}:y^2=\frac{x(x-\frac{n}{t})}{x+nt}$ has a rational point $(x,y)$ with $y \ne 0.$
How would I go about to solve this problem?