MathDB

N1

Part of 2016 Romanian Master of Mathematics Shortlist

Problems(1)

every quadratic non-residue modulo n is a primitive root modulo n.

Source: RMM Shortlist 2016 N1

7/4/2019
Determine all integers n≥3n \ge 3 whose decimal expansion has less than 2020 digits, such that every quadratic non-residue modulo nn is a primitive root modulo nn.
An integer aa is a quadratic non-residue modulo nn, if there is no integer bb such that a−b2a - b^2 is divisible by nn. An integer aa is a primitive root modulo nn, if for every integer bb relatively prime to n there is a positive integer kk such that ak−ba^k - b is divisible by nn.
number theoryprimitive rootQuadratic Residues