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Korea Junior Mathematics Olympiad
2016 Korea Junior Math Olympiad
5
prove polynomial
prove polynomial
Source: 2016 KJMO #5
November 14, 2016
polynomial
number theory
algebra
Problem Statement
n
∈
N
+
n \in \mathbb {N^+}
n
∈
N
+
Prove that the following equation can be expressed as a polynomial about
n
n
n
.
[
2
1
]
+
[
2
2
]
+
[
2
3
]
+
.
.
.
+
[
2
n
2
]
\left[2\sqrt {1}\right]+\left[2\sqrt {2}\right]+\left[2\sqrt {3}\right]+ . . . +\left[2\sqrt {n^2}\right]
[
2
1
]
+
[
2
2
]
+
[
2
3
]
+
...
+
[
2
n
2
]
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