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National and Regional Contests
Germany Contests
QEDMO
2006 QEDMO 3rd
8
8
Part of
2006 QEDMO 3rd
Problems
(1)
f(1) = 1 , f(1)+ f(2)+...+ f(n) = n^2f(n), f(1995) =?
Source: Norwegian Mathematical Olympiad 1995 - Abel Competition p1a
2/11/2020
Let a function
f
f
f
satisfy
f
(
1
)
=
1
f(1) = 1
f
(
1
)
=
1
and
f
(
1
)
+
f
(
2
)
+
.
.
.
+
f
(
n
)
=
n
2
f
(
n
)
f(1)+ f(2)+...+ f(n) = n^2f(n)
f
(
1
)
+
f
(
2
)
+
...
+
f
(
n
)
=
n
2
f
(
n
)
for all
n
ā
N
n \in N
n
ā
N
. Determine
f
(
1995
)
f(1995)
f
(
1995
)
.
algebra
function