I've recently been working on the following problem:
Is there a right angled triangle with rational side lengths and an area of $1$?
I was told I wouldn't be able to solve it, but this was simply an exercise to see how I go about solving problems.
I indeed was not able to solve, but was able to reduce it to a problem with an elliptic curve that I suspect relates to Fermat's last Theorem. However, I suspect there is a more subtle and simpler approach to the problem. So what exactly is the answer?