Imagine a right triangle with sides:
Long side C is $4n$, sides $b$ and $a$ are $2n$ and $n$, where $n$ is an integer.
How many right triangles are of this form?
My attempt:
$$16n^2 = 4n^2 + n^2$$ $$11n^2 = 0$$
$n$ is not an integer. No right triangles can be made this way.
Had this on an entrance exam for medicine...It seemed too obvious to be true...?