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 
)
