Counting quadratic nonresidues in shifted subsets of the set of quadratic nonresidues for primes \(p = 4 k + 1\) (Q1751338)

Summary: Let \(p = 4 k + 1\) be a prime number and \(\mathbb{F}_p\) the finite field with \(p\) elements. For \(x \in [\![ 1, n ]\!]\), \(N_x\) will denote the set of quadratic nonresidues less than or equal to \(x\). In this work we calculate the number of quadratic nonresidues in the shifted set \(N_{(p - 1) / 2} + a\).