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AIME 2024 / AIME 2024 train 3559b9ac-7936-5b75-b48f-1b965a2cba2e

Problem

Answer published by the source. Consult the official source to check your work against its answer.

Problem

Let ω≠1\omega \neq 1 be a 13th root of unity. Find the remainder when ∏k=012(2−2ωk+ω2k) \prod_{k=0}^{12}(2 - 2\omega^k + \omega^{2k}) is divided by 1000.
Plain-text mathematical notation (without MathML)
Let ω≠1 be a 13th root of unity. Find the remainder when 
∏_(k=0)¹²(2−2ω^(k)+ω^(2k)) is divided by 1000.
Original LaTeX notation
Let $\omega \neq 1$ be a 13th root of unity. Find the remainder when 
\[ \prod_{k=0}^{12}(2 - 2\omega^k + \omega^{2k}) \] is divided by 1000.

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Source and history

task_id
3559b9ac-7936-5b75-b48f-1b965a2cba2e
task_key
default--train--3559b9ac-7936-5b75-b48f-1b965a2cba2e
task_revision_id
3
config / split
default / train

Official source

initial import