[math-fun] Number of representations of N as sum of two squares

N=a^2+b^2>0 where a,b are integers (of either sign) #representations = 4*sum(over all divisors d of N) ( [1 if (d mod 4)=1 else 0] - [1 if (d mod 4)=3 else 0] ) I am not sure who first invented this nifty formula (Gauss?). It makes it clear, though, that #representations(N) < #divisors(N) < exp(log(2+o(1))*lnN/lnlnN).