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Regional Mathematical Olympiad
2024 India Regional Mathematical Olympiad
2
RMO 2024 Q2
RMO 2024 Q2
Source: RMO 2024 Q2
November 3, 2024
number theory
Problem Statement
For a positive integer
n
n
n
, let
R
(
n
)
R(n)
R
(
n
)
be the sum of the remainders when
n
n
n
is divided by
1
,
2
,
⋯
,
n
1,2, \cdots , n
1
,
2
,
⋯
,
n
. For example,
R
(
4
)
=
0
+
0
+
1
+
0
=
1
,
R(4) = 0 + 0 + 1 + 0 = 1,
R
(
4
)
=
0
+
0
+
1
+
0
=
1
,
R
(
7
)
=
0
+
1
+
1
+
3
+
2
+
1
+
0
=
8
R(7) = 0 + 1 + 1 + 3 + 2 + 1 + 0 = 8
R
(
7
)
=
0
+
1
+
1
+
3
+
2
+
1
+
0
=
8
. Find all positive integers such that
R
(
n
)
=
n
−
1
R(n) = n-1
R
(
n
)
=
n
−
1
.
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