Every prime factor of a number of the form
$$a^2+b^2$$
with gcd(a,b)=1 has -1 as a quadratic residue.
Does this work only for exponents with a common factor, or are there useful restrictions also for coprime exponents ?
For example , are there any restrictions for the prime factors of numbers of the form
$$a^4 + b^9$$
with gcd(a,b)=1 ?