Difference between revisions of "1976 IMO Problems/Problem 2"
(New page: == Problem == {{problem}} == Solution == {{solution}} == See also == {{IMO box|year=1976|num-b=1|num-a=3}}) |
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== Problem == | == Problem == | ||
| − | {{ | + | Let <math>P_{1}(x) = x^{2} - 2</math> and <math>P_{j}(x) = P_{1}(P_{j - 1}(x))</math> for <math>j= 2,\ldots</math> Prove that for any positive integer n the roots of the equation <math>P_{n}(x) = x</math> are all real and distinct. |
== Solution == | == Solution == | ||
Revision as of 10:37, 26 February 2008
Problem
Let 
and 
for 
Prove that for any positive integer n the roots of the equation 
are all real and distinct.
Solution
This problem needs a solution. If you have a solution for it, please help us out by adding it.
See also
| 1976 IMO (Problems) • Resources | ||
| Preceded by Problem 1 |
1 • 2 • 3 • 4 • 5 • 6 | Followed by Problem 3 |
| All IMO Problems and Solutions | ||
