MathDB
Complicated Functions

Source: 2019 AIME ii #8

March 22, 2019
AIMEAMCAIME IIfunction2019 AIME II2019 AMCPolynomials

Problem Statement

The polynomial f(z)=az2018+bz2017+cz2016f(z)=az^{2018}+bz^{2017}+cz^{2016} has real coefficients not exceeding 20192019, and f(1+3i2)=2015+20193if(\tfrac{1+\sqrt{3}i}{2})=2015+2019\sqrt{3}i. Find the remainder when f(1)f(1) is divided by 10001000.
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