VTMO 2026 - Grade 7 - Final - SET 3 - Self-study Question 4

Positive integers $k_1,k_2,k_3$ satisfy $k_1+k_2+k_3=2021$. Numbers $x_1,x_2,x_3$ satisfy $\frac{|x_1-x_2|}{k_1}=\frac{|x_2-x_3|}{k_2}=\frac{|x_3-x_1|}{k_3}$. Find $T=(x_1+x_2-2x_3)^{2021}$.