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Omni-MATH / Find all monic polynomials f with integer coefficients satisfying the following condition: there exists a positive integer N such that p divides 2(f(p)!)+1 for every prime p>N for …

Problem

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

problem

Find all monic polynomials ff with integer coefficients satisfying the following condition: there exists a positive integer NN such that pp divides 2(f(p)!)+12(f(p)!)+1 for every prime p>Np>N for which f(p)f(p) is a positive integer.
Plain-text mathematical notation (without MathML)
Find all monic polynomials f with integer coefficients satisfying the following condition: there exists a positive integer N such that p divides 2(f(p)!)+1 for every prime p>N for which f(p) is a positive integer.
Original LaTeX notation
Find all monic polynomials $f$ with integer coefficients satisfying the following condition: there exists a positive integer $N$ such that $p$ divides $2(f(p)!)+1$ for every prime $p>N$ for which $f(p)$ is a positive integer.

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Source and history

task_id
66a5569b-a0ee-599d-bcd3-05a940d363a2
task_key
test--66a5569b-a0ee-599d-bcd3-05a940d363a2
task_revision_id
1
config / split
/ test

Official source

initial import