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Polish MO Finals
1976 Polish MO Finals
6
6
Part of
1976 Polish MO Finals
Problems
(1)
f(n) = log_p n if f(kl) = f(k)+ f(l)
Source: Polish MO Finals 1976 p6
8/23/2024
An increasing function
f
:
N
→
R
f : N \to R
f
:
N
→
R
satisfies
f
(
k
l
)
=
f
(
k
)
+
f
(
l
)
f
o
r
a
l
l
k
,
l
∈
N
.
f(kl) = f(k)+ f(l)\,\,\, for \,\,\, all \,\,\, k,l \in N.
f
(
k
l
)
=
f
(
k
)
+
f
(
l
)
f
or
a
ll
k
,
l
∈
N
.
Show that there is a real number
p
>
1
p > 1
p
>
1
such that
f
(
n
)
=
l
o
g
p
n
f(n) =\ log_pn
f
(
n
)
=
l
o
g
p
n
for all
n
n
n
.
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