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Omni-MATH / Find all positive integers n<10¹⁰⁰ for which simultaneously n divides 2^(n), n−1 divides 2^(n)−1, and n−2 divides 2^(n)−2.

Problem

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problem

Find all positive integers n<10100n < 10^{100} for which simultaneously nn divides 2n2^n, n−1n-1 divides 2n−12^n-1, and n−2n-2 divides 2n−22^n - 2.
Plain-text mathematical notation (without MathML)
Find all positive integers n<10¹⁰⁰ for which simultaneously n divides 2^(n), n−1 divides 2^(n)−1, and n−2 divides 2^(n)−2.
Original LaTeX notation
Find all positive integers $n < 10^{100}$ for which simultaneously $n$ divides $2^n$, $n-1$ divides $2^n-1$, and $n-2$ divides $2^n - 2$.

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Source and history

task_id
d441679a-9893-5ce2-bb1b-c574a15d51a2
task_key
test--d441679a-9893-5ce2-bb1b-c574a15d51a2
task_revision_id
1
config / split
/ test

Official source

initial import