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Let be a function satisfying and
MATHEMATICS · Single correct · AoPS · Mathematics · Functions · Functions
Problem
Let
f
f
f
be a function satisfying
2
f
(
x
y
)
=
[
f
(
x
)
]
y
+
[
f
(
y
)
]
x
2f(xy)=[f(x)]^y+[f(y)]^x
2
f
(
x
y
)
=
[
f
(
x
)
]
y
+
[
f
(
y
)
]
x
and
f
(
1
)
=
k
≠
1
f(1)=k\ne1
f
(
1
)
=
k
=
1
. Then
∑
r
=
1
n
f
(
r
)
\sum_{r=1}^{n}f(r)
∑
r
=
1
n
f
(
r
)
is equal to (a)
k
n
−
1
k^n-1
k
n
−
1
(b)
k
n
k^n
k
n
(c)
k
n
+
1
k^n+1
k
n
+
1
(d) None of these
Related theory
Functions
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