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Omni-MATH / For a nonnegative integer k, let f(k) be the number of ones in the base 3 representation of k. Find all complex numbers z such that ∑_(k=0)^(3¹⁰¹⁰−1)(−2)^(f(k))(z+k)²⁰²³=0.

Problem

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problem

For a nonnegative integer kk, let f(k)f(k) be the number of ones in the base 3 representation of kk. Find all complex numbers zz such that ∑k=031010−1(−2)f(k)(z+k)2023=0. \sum_{k=0}^{3^{1010}-1} (-2)^{f(k)} (z+k)^{2023} = 0.
Plain-text mathematical notation (without MathML)
For a nonnegative integer k, let f(k) be the number of ones in the base 3 representation of k. Find all complex numbers z such that ∑_(k=0)^(3¹⁰¹⁰−1)(−2)^(f(k))(z+k)²⁰²³=0.
Original LaTeX notation
For a nonnegative integer $k$, let $f(k)$ be the number of ones in the base 3 representation of $k$. Find all complex numbers $z$ such that \[ \sum_{k=0}^{3^{1010}-1} (-2)^{f(k)} (z+k)^{2023} = 0. \]

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Source and history

task_id
d7557462-030a-518a-bf95-b07139b59020
task_key
test--d7557462-030a-518a-bf95-b07139b59020
task_revision_id
1
config / split
/ test

Official source

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