A Note on Quadratic Residuosity and UP

UP is the class of languages accepted by polynomial-time nondeterministic Turing machines that have at most one accepting path. We show that the quadratic residue problem belongs to UP ∩ coUP. This affirmatively answers an open problem, discussed in Theory of Computational Complexity (Du and Ko, 2000), of whether the quadratic nonresidue problem is in NP. We generalize to higher powers and sho