Difference between revisions of "2006 USAMO Problems/Problem 3"

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== Problem ==
 
== Problem ==
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For integral <math>m</math>, let <math>p(m)</math> be the greatest prime divisor of <math>m</math>. By convention, we set <math>p(\pm 1)=1</math> and <math>p(0)=\infty</math>. Find all polynomial <math>f</math> with integer coefficients such that the sequence
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<math>(p(f(n^2))-2n)_{n\ge 0}</math>
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is bounded above. (In particular, this requires <math>f(n^2)\neq 0</math> for <math>n\ge 0</math>)
 
== Solution ==
 
== Solution ==
 
== See Also ==
 
== See Also ==
 
*[[2006 USAMO Problems]]
 
*[[2006 USAMO Problems]]

Revision as of 11:03, 12 July 2006

Problem

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 polynomial $f$ with integer coefficients such that the sequence

$(p(f(n^2))-2n)_{n\ge 0}$

is bounded above. (In particular, this requires $f(n^2)\neq 0$ for $n\ge 0$)

Solution

See Also

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