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UKMT Senior Mathematical Challenge, 2019

Algebra Difficulty 3.0 AMC 10/12 Find the answer United Kingdom

A function $f$ satisfies the equation $(n-2019)f(n) - f(2019-n) = 2019$ for every integer $n$ . What is the value of $f(2019)$ ?

(A) $0$ (B) $1$ (C) $2018 \times 2019$ (D) $2019^2$ (E) $2019 \times 2020$

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