Difference between revisions of "2024 AIME II Problems/Problem 13"
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==Problem== | ==Problem== | ||
Let <math>\omega\neq 1</math> be a 13th root of unity. Find the remainder when | Let <math>\omega\neq 1</math> be a 13th root of unity. Find the remainder when | ||
| − | <cmath> | + | <cmath>\prod_{k=0}^{12}(2-2\omega^k+\omega^{2k})</cmath> |
| − | \prod_{k=0}^{12}(2-2\omega^k+\omega^{2k}) | ||
| − | </cmath> | ||
is divided by 1000. | is divided by 1000. | ||
Revision as of 23:33, 8 February 2024
Problem
Let 
be a 13th root of unity. Find the remainder when
![\[\prod_{k=0}^{12}(2-2\omega^k+\omega^{2k})\]](http://latex.artofproblemsolving.com/c/c/d/ccd8d560907cc70b8b51b8c189e2bbd61d7a08a8.png)
is divided by 1000.
