Primitive Roots and Quadratic Residues

2018 ◽  
pp. 283-315
Author(s):  
Antonio Caminha Muniz Neto
Keyword(s):  
Quadratic Residues ◽  
Primitive Roots

scholarly journals A LINEAR COMPLEXITY ANALYSIS OF QUADRATIC RESIDUES AND PRIMITIVE ROOTS SPACINGS

2019 ◽  
Vol 19 (1) ◽  
pp. 27-37
Author(s):  
Mihai Caragiu ◽  
Shannon Tefft ◽  
Aaron Kemats ◽  
Travis Maenle
Keyword(s):  
Linear Complexity ◽  
Complexity Analysis ◽  
Quadratic Residues ◽  
Primitive Roots

scholarly journals Polynomials that represent quadratic residues at primitive roots

1982 ◽  
Vol 98 (1) ◽  
pp. 123-137 ◽  
Author(s):  
Daniel Madden ◽  
William Vélez
Keyword(s):  
Quadratic Residues ◽  
Primitive Roots

APPLICATIONS OF LERCH’S THEOREM TO PERMUTATIONS OF QUADRATIC RESIDUES

2019 ◽  
Vol 100 (3) ◽  
pp. 362-371
Author(s):  
LI-YUAN WANG ◽  
HAI-LIANG WU
Keyword(s):  
Positive Integer ◽  
Quadratic Residues ◽  
Primitive Roots ◽  
Permutation Problems

Let $n$ be a positive integer and $a$ an integer prime to $n$. Multiplication by $a$ induces a permutation over $\mathbb{Z}/n\mathbb{Z}=\{\overline{0},\overline{1},\ldots ,\overline{n-1}\}$. Lerch’s theorem gives the sign of this permutation. We explore some applications of Lerch’s result to permutation problems involving quadratic residues modulo $p$ and confirm some conjectures posed by Sun [‘Quadratic residues and related permutations and identities’, Preprint, 2018, arXiv:1809.07766]. We also study permutations involving arbitrary $k$th power residues modulo $p$ and primitive roots modulo a power of $p$.

The distribution of primitive roots in finite fields

1990 ◽  
Vol 45 (1) ◽  
pp. 223-224 ◽  
Author(s):  
G I Perel'muter ◽  
I E Shparlinskii
Keyword(s):  
Finite Fields ◽  
Primitive Roots
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