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 le

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 http://en.wikipedia.org/wiki/Proofs_of_Fermat's_theorem_on_sums_of_two_squares http://en.wikipedia.org/wiki/Proofs_of_Fermat's_theorem_on_s...