TY - JOUR
T1 - Character sums and congruences with n!
AU - Garaev, Moubariz Z.
AU - Luca, Florian
AU - Shparlinski, Igor E.
PY - 2004/12
Y1 - 2004/12
N2 - We estimate character sums with n!, on average, and individually. These bounds are used to derive new results about various congruences modulo a prime p and obtain new information about the spacings between quadratic nonresidues modulo p. In particular, we show that there exists a positive integer n ≪ p1/2+ε such that n! is a primitive root modulo p. We also show that every nonzero congruence class a ≢ 0 (mod p) can be represented as a product of 7 factorials, a ≡ nI!...n7! (mod p), where max{ni
AB - We estimate character sums with n!, on average, and individually. These bounds are used to derive new results about various congruences modulo a prime p and obtain new information about the spacings between quadratic nonresidues modulo p. In particular, we show that there exists a positive integer n ≪ p1/2+ε such that n! is a primitive root modulo p. We also show that every nonzero congruence class a ≢ 0 (mod p) can be represented as a product of 7 factorials, a ≡ nI!...n7! (mod p), where max{ni
UR - http://www.scopus.com/inward/record.url?scp=10044289130&partnerID=8YFLogxK
U2 - 10.1090/S0002-9947-04-03612-8
DO - 10.1090/S0002-9947-04-03612-8
M3 - Article
AN - SCOPUS:10044289130
VL - 356
SP - 5089
EP - 5102
JO - Transactions of the American Mathematical Society
JF - Transactions of the American Mathematical Society
SN - 0002-9947
IS - 12
ER -