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Omni-MATH / ( Titu Andreescu, Gabriel Dospinescu ) 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…

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( Titu Andreescu, Gabriel Dospinescu ) For integral mm , let p(m)p(m) be the greatest prime divisor of mm . 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∈Z≥0\{ p(f(n^2))-2n) \}_{n \in \mathbb{Z} \ge 0} is bounded above. (In particular, this requires f(n2)≠0f(n^2)\neq 0 for n≥0n\ge 0 .)
Plain-text mathematical notation (without MathML)
( Titu Andreescu, Gabriel Dospinescu ) 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∈Z≥0) is bounded above. (In particular, this requires f(n²)≠0 for n≥0 .)
Original LaTeX notation
( Titu Andreescu, Gabriel Dospinescu ) 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 $\{ p(f(n^2))-2n) \}_{n \in \mathbb{Z} \ge 0}$ is bounded above. (In particular, this requires $f(n^2)\neq 0$ for $n\ge 0$ .)

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Source and history

task_id
56366250-fffd-5fdd-8dba-630e73f2d63f
task_key
test--56366250-fffd-5fdd-8dba-630e73f2d63f
task_revision_id
1
config / split
/ test

Official source

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