On sets which contain a qth power residue for almost all prime modules

Mariusz Ska/lba. "On sets which contain a qth power residue for almost all prime modules." Colloquium Mathematicae 102.1 (2005): 67-71. <http://eudml.org/doc/283742>.

@article{MariuszSka2005,
abstract = {A classical theorem of M. Fried [2] asserts that if non-zero integers $β₁,...,β_l$ have the property that for each prime number p there exists a quadratic residue $β_j$ mod p then a certain product of an odd number of them is a square. We provide generalizations for power residues of degree n in two cases: 1) n is a prime, 2) n is a power of an odd prime. The proofs involve some combinatorial properties of finite Abelian groups and arithmetic results of [3].},
author = {Mariusz Ska/lba},
journal = {Colloquium Mathematicae},
language = {eng},
number = {1},
pages = {67-71},
title = {On sets which contain a qth power residue for almost all prime modules},
url = {http://eudml.org/doc/283742},
volume = {102},
year = {2005},
}

TY - JOUR
AU - Mariusz Ska/lba
TI - On sets which contain a qth power residue for almost all prime modules
JO - Colloquium Mathematicae
PY - 2005
VL - 102
IS - 1
SP - 67
EP - 71
AB - A classical theorem of M. Fried [2] asserts that if non-zero integers $β₁,...,β_l$ have the property that for each prime number p there exists a quadratic residue $β_j$ mod p then a certain product of an odd number of them is a square. We provide generalizations for power residues of degree n in two cases: 1) n is a prime, 2) n is a power of an odd prime. The proofs involve some combinatorial properties of finite Abelian groups and arithmetic results of [3].
LA - eng
UR - http://eudml.org/doc/283742
ER -