Difference between revisions of "2022 SSMO Relay Round 4 Problems/Problem 2"
(Created page with "==Problem== The roots of <math>f(x)=x^3+5x+8</math> are <math>r_1,r_2,r_3.</math> Let <math>g_n(x)</math> be a polynomial with roots <math>r_1+n, r_2+n,r_3+n.</math> If<cmath>...") |
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Latest revision as of 13:11, 14 December 2023
Problem
The roots of 
are 
Let 
be a polynomial with roots 
If![\[S=\sum_{n=1}^{T}(-1)^{n}g_n(5),\]](http://latex.artofproblemsolving.com/d/4/5/d4599d33d3a9b9d0c86103b46aa54cff389988a7.png)
find the remainder when 
is divided by 1000.
