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1993 Moldova Team Selection Test
4
Solve in positive integers the following equation
Solve in positive integers the following equation
Source: Moldova TST 1993
August 8, 2023
equation
Problem Statement
Solve in positive integers the following equation
[
1
]
+
[
2
]
+
[
3
]
+
…
+
[
x
2
−
2
]
+
[
x
2
−
1
]
=
125
,
\left [\sqrt{1}\right]+\left [\sqrt{2}\right]+\left [\sqrt{3}\right]+\ldots+\left [\sqrt{x^2-2}\right]+\left [\sqrt{x^2-1}\right]=125,
[
1
]
+
[
2
]
+
[
3
]
+
…
+
[
x
2
−
2
]
+
[
x
2
−
1
]
=
125
,
where
[
a
]
[a]
[
a
]
is the integer part of the real number
a
a
a
.
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