论文标题
$ s $ - 线性复发序列术语的总和
$S$-parts of sums of terms of linear recurrence sequences
论文作者
论文摘要
令$ s = \ {p_1，\ ldots，p_s \} $为有限的，非空的质数集，$（u_ {n}）_ {n \ geq 0} $是订单$ r $的整数的线性复发序列。对于任何积极整数$ k，$我们定义$（u_j^{（k）}）_ {j \ geq 1} $由$ u_ {n_k} + \ cdots + u_ cdots + u_ {n_1}的整数组成的增加序列。 Under certain assumptions, we prove that for any $ε>0,$ there exists an integer $n_{0}$ such that $[U_j^{(k)}]_S < \left(U_j^{(k)}\right)^ε,$ for $ j > n_0,$ where $[m]_S$ denote the $S$-part of the positive integer $m$. On further assumptions on $(U_{n})_{n \geq 0},$ we also compute an effective bound for $[U_j^{(k)}]_S$ of the form $\left(U_j^{(k)}\right)^{1-c}$, where $c $ is a positive constant depends only on $(U_{n})_{n \ geq 0} $和$S。$
Let $S= \{ p_1, \ldots, p_s\}$ be a finite, non-empty set of distinct prime numbers and $(U_{n})_{n \geq 0}$ be a linear recurrence sequence of integers of order $r$. For any positive integer $k,$ we define $(U_j^{(k)})_{j\geq 1}$ an increasing sequence composed of integers of the form $U_{n_k} +\cdots + U_{n_1}, \ n_k>\cdots >n_1$. Under certain assumptions, we prove that for any $ε>0,$ there exists an integer $n_{0}$ such that $[U_j^{(k)}]_S < \left(U_j^{(k)}\right)^ε,$ for $ j > n_0,$ where $[m]_S$ denote the $S$-part of the positive integer $m$. On further assumptions on $(U_{n})_{n \geq 0},$ we also compute an effective bound for $[U_j^{(k)}]_S$ of the form $\left(U_j^{(k)}\right)^{1-c}$, where $c $ is a positive constant depends only on $(U_{n})_{n \geq 0}$ and $S.$
