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AIME 2024 / AIME 2024 train 1f1ae340-94af-59d2-af93-f54360abec74

Problem

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

Problem

Let

p

be the least prime number for which there exists a positive integer

n

such that

n^{4}+1

is divisible by

p^{2}

. Find the least positive integer

m

such that

m^{4}+1

is divisible by

p^{2}

Plain-text mathematical notation (without MathML)

Let p be the least prime number for which there exists a positive integer n such that n⁴+1 is divisible by p². Find the least positive integer m such that m⁴+1 is divisible by p².

Original LaTeX notation

Let $p$ be the least prime number for which there exists a positive integer $n$ such that $n^{4}+1$ is divisible by $p^{2}$. Find the least positive integer $m$ such that $m^{4}+1$ is divisible by $p^{2}$.

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Source and history

task_id: 1f1ae340-94af-59d2-af93-f54360abec74
task_key: default--train--1f1ae340-94af-59d2-af93-f54360abec74
task_revision_id: 2
config / split: default / train

Official source

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