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1978 IMO Longlists
18
18
Part of
1978 IMO Longlists
Problems
(1)
Inequality on number of lattice points
Source:
10/20/2010
Given a natural number
n
n
n
, prove that the number
M
(
n
)
M(n)
M
(
n
)
of points with integer coordinates inside the circle
(
O
(
0
,
0
)
,
n
)
(O(0, 0),\sqrt{n})
(
O
(
0
,
0
)
,
n
)
satisfies
π
n
−
5
n
+
1
<
M
(
n
)
<
π
n
+
4
n
+
1
\pi n - 5\sqrt{n} + 1<M(n) < \pi n+ 4\sqrt{n} + 1
πn
−
5
n
+
1
<
M
(
n
)
<
πn
+
4
n
+
1
inequalities
analytic geometry
number theory unsolved
number theory