This story mentions Fermat's theorem that every prime congruent to 1 modulo 4 is a sum of two squares. Fermat provided no proof of this theorem. There are at least four different proofs, attributable to Euler, Lagrange, Dedekind and Zagier. See <a href="http://en.wikipedia.org/wiki/Proofs_of_Fermat's_theorem_on_sums_of_two_squares" rel="nofollow">http://en.wikipedia.org/wiki/Proofs_of_Fermat's_theorem_on_s...</a>