2021/11/09 by Shivarajkumar
#11A07 #11B75 #FOS: Mathematics #G.2 #Number Theory (math.NT)
paper · doi:10.48550/arxiv.2111.05219
In this paper, if prime p≡ 3\pmod 4 is sufficiently large then we prove an upper bound on the number of occurences of any arbitrary pattern of quadratic residues and nonresidues of length k as k tends to \lceil log2 p\rceil. As an immediate consequence, it proves that, there exist a constant c such that, the least nonresidue for such primes is at most c\lceil log2 p\rceil.