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MathNet 2020 — Math Olympiad Vault — Part 01 Question 24

Math Olympiad Vault · MathNet 2020 — Math Olympiad Vault — Part 01

Question 24

Find all real numbers $x$ that satisfy the equation
$$
\frac{x-2020}{1}+\frac{x-2019}{2}+\cdots+\frac{x-2000}{21}=\frac{x-1}{2020}+\frac{x-2}{2019}+\cdots+\frac{x-21}{2000},
$$
and simplify your answer(s) as much as possible. Justify your solution.