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2023 Kyiv City MO Round 1
Problem 1
Best algebra in the history of MO
Best algebra in the history of MO
Source: Kyiv City MO 2023 Round 1, Problem 9.1
December 16, 2023
algebra
Problem Statement
Find the integer which is closest to the value of the following expression:
(
(
3
+
1
)
2023
−
(
1
3
−
1
)
2023
)
⋅
(
(
3
+
2
)
2023
−
(
1
3
−
2
)
2023
)
⋅
…
⋅
(
(
3
+
8
)
2023
−
(
1
3
−
8
)
2023
)
\left((3 + \sqrt{1})^{2023} - \left(\frac{1}{3 - \sqrt{1}}\right)^{2023} \right) \cdot \left((3 + \sqrt{2})^{2023} - \left(\frac{1}{3 - \sqrt{2}}\right)^{2023} \right) \cdot \ldots \cdot \left((3 + \sqrt{8})^{2023} - \left(\frac{1}{3 - \sqrt{8}}\right)^{2023} \right)
(
(
3
+
1
)
2023
−
(
3
−
1
1
)
2023
)
⋅
(
(
3
+
2
)
2023
−
(
3
−
2
1
)
2023
)
⋅
…
⋅
(
(
3
+
8
)
2023
−
(
3
−
8
1
)
2023
)
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