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- W3005920350 abstract "Given a prime $pge 5$, and given $1<kappa<p-1$, we call a sequence $(a_n)_{n}$ in $mathbb{F}_p$ a $Phi_{kappa}$-sequence if it is periodic with period $p-1$, and if it satisfies the linear recurrence $a_n+a_{n+1}=a_{n+kappa}$ with $a_0=1$. Such a sequence is said to be a complete $Phi_{kappa}$-sequence if in addition ${a_0,a_1,...,a_{p-2}}={1,...,p-1}$. For instance, every primitive root $b$ mod $p$ generates a complete $Phi_{kappa}$-sequence $a_n=b^n$ for some (unique) $kappa$. A natural question is whether every complete $Phi_{kappa}$-sequence is necessarily defined by a primitive root. For $kappa=2$ the answer is known to be positive. In this paper we reexamine that case and investigate the case $kappa=3$ together with the associated cases $kappa=p-2$ and $kappa=p-3$." @default.
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- W3005920350 date "2006-05-01" @default.
- W3005920350 modified "2023-09-23" @default.
- W3005920350 title "Complete padovan sequences in finite fields" @default.
- W3005920350 hasPublicationYear "2006" @default.
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