2019 AIME I Problems/Problem 10
The 2019 AIME I takes place on March 13, 2019.
Problem 10
For distinct complex numbers 
, the polynomial
![\[(x-z_1)^3(x-z_2)^3 \cdots (x-z_{673})^3\]](http://latex.artofproblemsolving.com/3/5/b/35b2995ac0fe946045c887ed51b6c5a4920ade87.png)
can be expressed as 
, where 
is a polynomial with complex coefficients and with degree at most 
. The value of
![\[\left| \sum_{1 \le j <k \le 673} z_jz_k \right|\]](http://latex.artofproblemsolving.com/8/f/4/8f41f0be45a01d496350a366e307c73e63020126.png)
can be expressed in the form 
, where 
and 
are relatively prime positive integers. Find 
.
Solution
See Also
| 2019 AIME I (Problems • Answer Key • Resources) | ||
| Preceded by Problem 9 |
Followed by Problem 11 | |
| 1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 | ||
| All AIME Problems and Solutions | ||
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions. 
