ISL 2003 N1
Posted: Tue Aug 16, 2016 12:50 am
Let $m$ be a fixed integer greater than $1$. The sequence $x_0$, $x_1$, $x_2$, $\ldots$ is defined as follows:
$x_i= 2^i$ if $0 \leq i\leq m-1$ and $x_i = \sum_{j=1}^{m}x_{i-j},$ if $i\geq m$.
Find the greatest $k$ for which the sequence contains $k$ consecutive terms divisible by $m$
$x_i= 2^i$ if $0 \leq i\leq m-1$ and $x_i = \sum_{j=1}^{m}x_{i-j},$ if $i\geq m$.
Find the greatest $k$ for which the sequence contains $k$ consecutive terms divisible by $m$