Fermi
·
Concept Library
·
Courses
·
Books
·
Problems
·
Simulations
·
Math Wiki
·
High School
Fermi
›
Problems
Mathematics
Mathematics
Problem
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, \dots, 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
n
n
n
such that
R
(
n
)
=
n
−
1
R(n) = n - 1
R
(
n
)
=
n
−
1
.
Browse the problem library