Configurations Of Consecutive Primitive Roots

Abstract

Let $p\ge 2$ be a large prime, and let $k\ll \log p$ be a small integer. This note proves the existence of various configurations of $(k+1)$-tuples of consecutive and quasi consecutive primitive roots $n+a_0,n+a_1,n+a_2,\dots ,n+a_k$ in the finite field ${\mathbb{F}}_p$, where $a_0,a_1,\dots ,a_k$ is a fixed $(k+1)$-tuples of distinct integers.

Forty Five Pages. Keywords: Primitive root; Consecutive primitive root; Consecutive Squarefree primitive root; Relative prime primitive root

References in corpus (4)

• Consecutive primes in tuples
• New estimates of double trigonometric sums with exponential functions
• On Gaps Between Primitive Roots in the Hamming Metric
• Primitive Roots In Short Intervals

Cited by in corpus (1)

• Simultaneous Elements Of Prescribed Multiplicative Orders