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Omni-MATH / Find all the pairs of positive integers (x,p) such that p is a prime, x≤2p and x^(p−1) is a divisor of (p−1)^(x)+1.

Problem

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problem

Find all the pairs of positive integers (x,p)(x,p) such that p is a prime, x≤2px \leq 2p and xp−1x^{p-1} is a divisor of (p−1)x+1 (p-1)^{x}+1.
Plain-text mathematical notation (without MathML)
Find all the pairs of positive integers (x,p) such that p is a prime, x≤2p and x^(p−1) is a divisor of (p−1)^(x)+1.
Original LaTeX notation
Find all the pairs of positive integers $(x,p)$ such that p is a prime, $x \leq 2p$ and $x^{p-1}$ is a divisor of $ (p-1)^{x}+1$.

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Source and history

task_id
7215c953-e8b6-502e-a09e-cb782cdb1645
task_key
test--7215c953-e8b6-502e-a09e-cb782cdb1645
task_revision_id
1
config / split
/ test

Official source

initial import