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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...
This paper presents some hypotheses and theorems concerning the least primitive roots modulo prime number, particularly the hypotheses about mean value of the least primitive root and order of its value. The verification of these hypotheses was done by a computer for numbers less then 2 · 10 9.
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