MathDB
Polynomial

Source: 2005 National High School Mathematics League, Exam One, Problem 7

March 19, 2020
algebrapolynomial

Problem Statement

The polynomial f(x)=1−x+x2−x3+⋯−x19+x20f(x)=1-x+x^2-x^3+\cdots-x^{19}+x^{20} is written into the form g(y)=a0+a1y+a2y2+⋯+a20y20g(y)=a_0+a_1y+a_2y^2+\cdots+a_{20}y^{20}, where y=x−4y=x-4, then a0+a1+⋯+a20=a_0+a_1+\cdots+a_{20}=________.
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