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Kvant Problems
Kvant 2021
M2663
M2663
Part of
Kvant 2021
Problems
(1)
Silk Road 2021 P2
Source:
6/28/2021
For every positive integer
m
m
m
prove the inquality
∣
{
m
}
−
1
2
∣
≥
1
8
(
m
+
1
)
|\{\sqrt{m}\} - \frac{1}{2}| \geq \frac{1}{8(\sqrt m+1)}
∣
{
m
}
−
2
1
∣
≥
8
(
m
+
1
)
1
(The integer part
[
x
]
[x]
[
x
]
of the number
x
x
x
is the largest integer not exceeding
x
x
x
. The fractional part of the number
x
x
x
is a number
{
x
}
\{x\}
{
x
}
such that
[
x
]
+
{
x
}
=
x
[x]+\{x\}=x
[
x
]
+
{
x
}
=
x
.)A. Golovanov
algebra
inquality