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Omni-MATH / Let m be a fixed integer greater than 1. The sequence x₀, x₁, x₂, … is defined as follows: …

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problem

Let mm be a fixed integer greater than 11. The sequence x0x_0, x1x_1, x2x_2, …\ldots is defined as follows: \[x_i = \begin{cases}2^i&\text{if }0\leq i \leq m - 1;\\\sum_{j=1}^mx_{i-j}&\text{if }i\geq m.\end{cases}\] Find the greatest kk for which the sequence contains kk consecutive terms divisible by mm . [i]
Plain-text mathematical notation (without MathML)
Let m be a fixed integer greater than 1. The sequence x₀, x₁, x₂, … is defined as follows: 
\[x_i = \begin{cases}2^i&\text{if }0\leq i \leq m - 1;\\\sum_{j=1}^mx_{i-j}&\text{if }i\geq m.\end{cases}\]
Find the greatest k for which the sequence contains k consecutive terms divisible by m .

[i]
Original LaTeX notation
Let $m$ be a fixed integer greater than $1$. The sequence $x_0$, $x_1$, $x_2$, $\ldots$ is defined as follows: 
\[x_i = \begin{cases}2^i&\text{if }0\leq i \leq m - 1;\\\sum_{j=1}^mx_{i-j}&\text{if }i\geq m.\end{cases}\]
Find the greatest $k$ for which the sequence contains $k$ consecutive terms divisible by $m$ .

[i]

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Source and history

task_id
e00cc56f-d7fc-5b70-bb90-39db25f2872f
task_key
test--e00cc56f-d7fc-5b70-bb90-39db25f2872f
task_revision_id
1
config / split
/ test

Official source

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