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Let p = 4 k + 1 be a prime number and F p the finite field with p elements. For x ∈ 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 .

Counting Quadratic Nonresidues in Shifted Subsets of the Set of Quadratic Nonresidues for Primes p = 4 k + 1