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Omni-MATH / A sequence of positive integers a₁,a₂,…,a₂₀₁₇ has the property that for all integers m where 1≤m≤2017,3(∑_(i=1)^(m)a_(i))²=∑_(i=1)^(m)a_(i)³. Compute a₁₃₃₇.

Problem

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problem

A sequence of positive integers a1,a2,…,a2017a_{1}, a_{2}, \ldots, a_{2017} has the property that for all integers mm where 1≤m≤2017,3(∑i=1mai)2=∑i=1mai31 \leq m \leq 2017,3\left(\sum_{i=1}^{m} a_{i}\right)^{2}=\sum_{i=1}^{m} a_{i}^{3}. Compute a1337a_{1337}.
Plain-text mathematical notation (without MathML)
A sequence of positive integers a₁,a₂,…,a₂₀₁₇ has the property that for all integers m where 1≤m≤2017,3(∑_(i=1)^(m)a_(i))²=∑_(i=1)^(m)a_(i)³. Compute a₁₃₃₇.
Original LaTeX notation
A sequence of positive integers $a_{1}, a_{2}, \ldots, a_{2017}$ has the property that for all integers $m$ where $1 \leq m \leq 2017,3\left(\sum_{i=1}^{m} a_{i}\right)^{2}=\sum_{i=1}^{m} a_{i}^{3}$. Compute $a_{1337}$.

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Source and history

task_id
76179c19-3fb2-52f1-862b-9ca6dfe112e8
task_key
test--76179c19-3fb2-52f1-862b-9ca6dfe112e8
task_revision_id
1
config / split
/ test

Official source

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