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National and Regional Contests
Turkey Contests
JBMO TST - Turkey
2022 JBMO TST - Turkey
2
2
Part of
2022 JBMO TST - Turkey
Problems
(1)
Solve x*[x]+2022=[x^2]
Source: 2022 Turkey JBMO TST P2
3/15/2022
For a real number
a
a
a
,
[
a
]
[a]
[
a
]
denotes the largest integer not exceeding
a
a
a
. Find all positive real numbers
x
x
x
satisfying the equation
x
ā
[
x
]
+
2022
=
[
x
2
]
x\cdot [x]+2022=[x^2]
x
ā
[
x
]
+
2022
=
[
x
2
]
algebra
floor function