There's a nice characterization of sums of two squares in terms of their prime factorization), namely that all primes of form 4k+3 appear with even multiplicity

There's a nice characterization of sums of two squares in terms of their prime factorization), namely that all primes of form 4k+3 appear with even multiplicity. From a quick look through OEIS it looks like there are similar characterizations for a^2 + n*b^2 but this is where I tap out on number theory.