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

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== Problem == | == Problem == | ||

+ | 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 | ||

+ | |||

+ | <math>(p(f(n^2))-2n)_{n\ge 0}</math> | ||

+ | |||

+ | 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 , let be the greatest prime divisor of . By convention, we set and . Find all polynomial with integer coefficients such that the sequence

is bounded above. (In particular, this requires for )