While browsing on internet for different proofs of Fermat's theorem on sums of two squares, I came across Zagier's "one-sentence proof" which seems to be the most elegant and short proof. It invokes a proof technique, I am not familiar with. So I would like to see different applications of this proof technique.
Are there theorems/problems besides Fermat's theorem on sums of two squares which can be solved using the similar technique.
PS: Please mention a suitable hint for the problem you pose. Thanks in advance.