On the distribution of quadratic residues and nonresidues modulo a prime number

@article{Peralta1992OnTD,
  title={On the distribution of quadratic residues and nonresidues modulo a prime number},
  author={Ren{\'e} C. Peralta},
  journal={Mathematics of Computation},
  year={1992},
  volume={58},
  pages={433-440}
}
Let P be a prime number and al, at be distinct integers modulo P. Let x be chosen at random with uniform distribution in Zp , and let yi = x + ai . We prove that the joint distribution of the quadratic characters of the yi 's deviates from the distribution of independent fair coins by no more than t(3 + xfi-)/P. That is, the probability of (Yi, ...Y, t) matching any particular quadratic character sequence of length t is in the range (I )t i t(3 + v/ii)/P. We establish the implications of this… Expand
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