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Omni-MATH / For integral m, let p(m) be the greatest prime divisor of m. By convention, we set p(±1)=1 and p(0)=∞. Find all polynomials f with integer coefficients such that the sequence …

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problem

For integral mm, let p(m)p(m) be the greatest prime divisor of m.m. By convention, we set p(±1)=1p(\pm 1) = 1 and p(0)=∞.p(0) = \infty. Find all polynomials ff with integer coefficients such that the sequence {p(f(n2))−2n}n≥0 \{p \left( f \left( n^2 \right) \right) - 2n \}_{n \geq 0} is bounded above. (In particular, this requires f(n2)≠0f \left (n^2 \right ) \neq 0 for n≥0.n \geq 0.)
Plain-text mathematical notation (without MathML)
For integral m, let p(m) be the greatest prime divisor of m. By convention, we set p(±1)=1 and p(0)=∞. Find all polynomials f with integer coefficients such that the sequence
{p(f(n²))−2n}_(n≥0) is bounded above. (In particular, this requires f(n²)≠0 for n≥0.)
Original LaTeX notation
For integral $m$, let $p(m)$ be the greatest prime divisor of $m.$ By convention, we set $p(\pm 1) = 1$ and $p(0) = \infty.$ Find all polynomials $f$ with integer coefficients such that the sequence
\[ \{p \left( f \left( n^2 \right) \right) - 2n \}_{n \geq 0}  \] is bounded above. (In particular, this requires $f \left (n^2 \right ) \neq 0$ for $n \geq 0.$)

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Source and history

task_id
8b36cc32-276a-5637-ada0-2d23a8424c22
task_key
test--8b36cc32-276a-5637-ada0-2d23a8424c22
task_revision_id
1
config / split
/ test

Official source

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