A note on n! modulo p

被引：6

作者：

Garaev, M. Z. ^{[1
]}

Hernandez, J. ^{[1
]}

机构：

[1] Univ Nacl Autonoma Mexico, Ctr Ciencias Matemat, Morelia 58089, Michoacan, Mexico

来源：

MONATSHEFTE FUR MATHEMATIK | 2017年 / 182卷 / 01期

关键词：

Factorials; Congruences; Exponential and character sums; Additive combinatorics; POINTS; CURVES; SUMS;

D O I：

10.1007/s00605-015-0867-8

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Let p be a prime, epsilon > 0 and 0 < L + 1 < L + N < p. We prove that if p(1/2+epsilon) < N < p(1-epsilon), then #{n! (mod p); L + 1 <= n <= L + N} > c( N log N)(1/2), c = c(epsilon) > 0. We use this bound to show that any lambda not equivalent to 0 (mod p) can be represented in the form lambda = n(1)!...n(7)! (mod p), where n(i) = o(p(11/12)). This refines the previously known range for n(i).

引用

页码：23 / 31

页数：9