2022 USAJMO Problems/Problem 6
Problem
Let 
be complex numbers, and define
![\[a_{n+1}=a_n^2+2b_nc_n\]](http://latex.artofproblemsolving.com/c/a/4/ca4a66b31e3c693419b2771c78287d9c589fa2f5.png)
![\[b_{n+1}=b_n^2+2c_na_n\]](http://latex.artofproblemsolving.com/4/6/3/463e0666030d03bba947553e814096c91db2b329.png)
![\[c_{n+1}=c_n^2+2a_nb_n\]](http://latex.artofproblemsolving.com/5/e/c/5eceeed057fdd37716fb322b3962ee36433d75ab.png)
for all nonnegative integers 
.
Suppose that 
for all . Prove that
![\[|a_0|^2+|b_0|^2+|c_0|^2\leq 1.\]](http://latex.artofproblemsolving.com/f/a/d/fad6f3579e7bc550cc761eaa40aa09481da67745.png)
Solution
Why is there nothing here?
See Also
| 2022 USAJMO (Problems • Resources) | ||
| Preceded by Problem 5 |
Followed by Last Question | |
| 1 • 2 • 3 • 4 • 5 • 6 | ||
| All USAJMO Problems and Solutions | ||
These problems are copyrighted © by the Mathematical Association of America, as part of the American Mathematics Competitions. 
