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Regional Mathematical Olympiad
2018 India Regional Mathematical Olympiad
2
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Source: RMO 2018 P2
October 7, 2018
algebra
Problem Statement
Let
n
n
n
be a natural number. Find all real numbers
x
x
x
satisfying the equation
∑
k
=
1
n
k
x
k
1
+
x
2
k
=
n
(
n
+
1
)
4
.
\sum^n_{k=1}\frac{kx^k}{1+x^{2k}}=\frac{n(n+1)}4.
k
=
1
∑
n
1
+
x
2
k
k
x
k
=
4
n
(
n
+
1
)
.
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