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C/1
2020 BAMO-8: C, BAMO-12: 1 Equation
2020 BAMO-8: C, BAMO-12: 1 Equation
Source:
February 27, 2020
Problem Statement
Find all real numbers
x
x
x
that satisfy the equation
x
−
2020
1
+
x
−
2019
2
+
⋯
+
x
−
2000
21
=
x
−
1
2020
+
x
−
2
2019
+
⋯
+
x
−
21
2000
,
\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},
1
x
−
2020
+
2
x
−
2019
+
⋯
+
21
x
−
2000
=
2020
x
−
1
+
2019
x
−
2
+
⋯
+
2000
x
−
21
,
and simplify your answer(s) as much as possible. Justify your solution.
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