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Omni-MATH / Let S be the set of 3⁴ points in four-dimensional space where each coordinate is in {−1,0,1}. Let N be the number of sequences of points P₁,P₂,…,P₂₀₂₀ in S such that P_(i)P_(i+1)=2…

Problem

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problem

Let SS be the set of 343^{4} points in four-dimensional space where each coordinate is in {−1,0,1}\{-1,0,1\}. Let NN be the number of sequences of points P1,P2,…,P2020P_{1}, P_{2}, \ldots, P_{2020} in SS such that PiPi+1=2P_{i} P_{i+1}=2 for all 1≤i≤20201 \leq i \leq 2020 and P1=(0,0,0,0)P_{1}=(0,0,0,0). (Here P2021=P1P_{2021}=P_{1}.) Find the largest integer nn such that 2n2^{n} divides NN.
Plain-text mathematical notation (without MathML)
Let S be the set of 3⁴ points in four-dimensional space where each coordinate is in {−1,0,1}. Let N be the number of sequences of points P₁,P₂,…,P₂₀₂₀ in S such that P_(i)P_(i+1)=2 for all 1≤i≤2020 and P₁=(0,0,0,0). (Here P₂₀₂₁=P₁.) Find the largest integer n such that 2^(n) divides N.
Original LaTeX notation
Let $S$ be the set of $3^{4}$ points in four-dimensional space where each coordinate is in $\{-1,0,1\}$. Let $N$ be the number of sequences of points $P_{1}, P_{2}, \ldots, P_{2020}$ in $S$ such that $P_{i} P_{i+1}=2$ for all $1 \leq i \leq 2020$ and $P_{1}=(0,0,0,0)$. (Here $P_{2021}=P_{1}$.) Find the largest integer $n$ such that $2^{n}$ divides $N$.

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Source and history

task_id
8a5f4fa7-2a47-5103-9647-ddb209442c54
task_key
test--8a5f4fa7-2a47-5103-9647-ddb209442c54
task_revision_id
1
config / split
/ test

Official source

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