论文标题
关于卢卡斯序列的外观等级的分裂性
On the divisibility of the rank of appearance of a Lucas sequence
论文作者
论文摘要
令$ u =（u_n）_ {n \ geq 0} $为lucas序列，对于每个素数$ p $，让$ρ_U（p）$是$ u $中的$ p $的排名此外，让$ d $是一个奇怪的积极整数。在一些温和的假设下，我们证明了用于Primes $ p \ leq X $数量的渐近公式，因此$ d $ diviles $ρ_U（p）$，为$ x \ to +\ \ iffty $。
Let $U = (U_n)_{n \geq 0}$ be a Lucas sequence and, for every prime number $p$, let $ρ_U(p)$ be the rank of appearance of $p$ in $U$, that is, the smallest positive integer $k$ such that $p$ divides $U_k$, whenever it exists. Furthermore, let $d$ be an odd positive integer. Under some mild hypotheses, we prove an asymptotic formula for the number of primes $p \leq x$ such that $d$ divides $ρ_U(p)$, as $x \to +\infty$.
