Difference between revisions of "2006 USAMO Problems/Problem 3"
Ragnarok23 (talk | contribs) |
(Standardized) |
||
| Line 1: | Line 1: | ||
== Problem == | == Problem == | ||
| − | |||
| − | <math>(p(f(n^2))-2n)_{n\ge 0}</math> | + | For integral <math>\displaystyle m </math>, let <math> \displaystyle p(m) </math> be the greatest prime divisor of <math> \displaystyle m </math>. By convention, we set <math> p(\pm 1)=1</math> and <math>p(0)=\infty</math>. Find all polynomials <math>\displaystyle 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 == | ||
| + | |||
| + | {{solution}} | ||
| + | |||
== See Also == | == See Also == | ||
| − | *[[2006 USAMO Problems]] | + | |
| + | * [[2006 USAMO Problems]] | ||
| + | * [http://www.artofproblemsolving.com/Forum/viewtopic.php?p=490625#p490625 Discussion on AoPS/MathLinks] | ||
| + | |||
| + | [[Category:Olympiad Number Theory Problems]] | ||
Revision as of 19:37, 1 September 2006
Problem
For integral 
, let 
be the greatest prime divisor of . By convention, we set 
and 
. Find all polynomials 
with integer coefficients such that the sequence 
is bounded above. (In particular, this requires 
for 
.)
Solution
This problem needs a solution. If you have a solution for it, please help us out by adding it.
