Upsetting Pitagoras
Why do this problem?
No knowledge is needed here, only mathematical reasoning. It is an
important point to make that finding a method for producing
solutions does not prove that there is no other method and no
smaller solution generated another way. However, once
you have found what you believe to be the smallest solution, it is
possible to check numerically that there are in fact no smaller
solutions.
Key question
Can you in any way use $a$, $b$ and $c$ where you know $a^2 + b^2 =
c^2$?
When you find a method for producing
solutionscan you be certain it is the only
possible method?