Difference between revisions of "2015 OIM Problems/Problem 3"
(Created page with "== Problem == Let <math>\alpha</math> and <math>\beta</math> be roots of the polynomial <math>x^2-qx+1</math>, where <math>q</math> is a rational number greater than 2. We de...") |
(→See also) |
||
| Line 12: | Line 12: | ||
== See also == | == See also == | ||
| + | [[OIM Problems and Solutions]] | ||
Latest revision as of 14:05, 14 December 2023
Problem
Let 
and 
be roots of the polynomial 
, where 
is a rational number greater than 2. We define 
, 
, and for each integer 
,
![\[s_n=\alpha ^n +\beta ^n,\;t_n=s_{n-1}+2s_{n-2}+\cdots+(n-1)s_1+n\]](http://latex.artofproblemsolving.com/2/0/9/209d7e4fa6633f8e0745828869f209151bf94daa.png)
Show that for all odd 
, 
is the square of a rational number.
~translated into English by Tomas Diaz. ~orders@tomasdiaz.com
Solution
This problem needs a solution. If you have a solution for it, please help us out by adding it.
