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Omni-MATH / Determine whether or not there exists a positive integer k such that p=6k+1 is a prime and binom{3k}{k} equiv 1 pmod{p}.

Problem

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problem

Determine whether or not there exists a positive integer

k

such that

p = 6k+1

is a prime and \[\binom{3k}{k} \equiv 1 \pmod{p}.\]

Plain-text mathematical notation (without MathML)

Determine whether or not there exists a positive integer k such that p=6k+1 is a prime and
\[\binom{3k}{k} \equiv 1  \pmod{p}.\]

Original LaTeX notation

Determine whether or not there exists a positive integer $k$ such that $p = 6k+1$ is a prime and
\[\binom{3k}{k} \equiv 1  \pmod{p}.\]

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task_id: a6ae156d-fe95-5684-9403-e1b60a100cb8
task_key: test--a6ae156d-fe95-5684-9403-e1b60a100cb8
task_revision_id: 4
config / split: / test

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