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MMLU-Pro / 8620 / Find all positive integers n<2²⁵⁰ for which simultaneously n divides…

Problem

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

question

Find all positive integers n<2250n<2^{250} for which simultaneously nn divides 2n2^n, n−1n-1 divides 2n−12^n-1, and n−2n-2 divides 2n−22^n - 2. Return all positive integers as an ascending list.
Plain-text mathematical notation (without MathML)
Find all positive integers n<2²⁵⁰ for which simultaneously n divides 2^(n), n−1 divides 2^(n)−1, and n−2 divides 2^(n)−2. Return all positive integers as an ascending list.
Original LaTeX notation
Find all positive integers $n<2^{250}$ for which simultaneously $n$ divides $2^n$, $n-1$ divides $2^n-1$, and $n-2$ divides $2^n - 2$. Return all positive integers as an ascending list.

category

math

options

  1. [1, 4, 16384]
  2. [5, 25, 1048576]
  3. [2, 8, 32768]
  4. [3, 9, 196608]
  5. [6, 24, 786432]
  6. [4, 16, 65536]
  7. [7, 14, 524288]
  8. [1, 8, 327680]
  9. [2, 16, 262144]
  10. [8, 32, 131072]

src

theoremQA-Math

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Source and history

upstream_id / Original problem ID
8620
task_id
7cd67b3c-2216-518c-9785-762f3c5e98c7
task_key
default--test--8620
task_revision_id
1
config / split
default / test

Official source

initial import