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On the average of the least quadratic non-residue modulo a prime number

Paszkiewicz A.

Electronics and Telecommunications Quarterly

2009

Vol. 55, No 4

639-647

In this paper we focus on a problem of existence the mean value of the least quadratic non-residue modulo a prime number. We prove that the answer to that question is positive and calculate the exact value of that constant with high accuracy. We also prove that the density of all primes having its least quadratic non-residue equal to k-th prime is 1/2k. Some computational results are included to provide numerical arguments that the convergence is very fast.