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National and Regional Contests
Netherlands Contests
Dutch IMO TST
2014 Dutch IMO TST
1
Function with prime divisors
Function with prime divisors
Source: Dutch IMO TST II Problem 1
July 17, 2014
function
algebra unsolved
algebra
Problem Statement
Let
f
:
Z
>
0
→
R
f:\mathbb{Z}_{>0}\rightarrow\mathbb{R}
f
:
Z
>
0
→
R
be a function such that for all
n
>
1
n > 1
n
>
1
there is a prime divisor
p
p
p
of
n
n
n
such that
f
(
n
)
=
f
(
n
p
)
−
f
(
p
)
.
f(n)=f\left(\frac{n}{p}\right)-f(p).
f
(
n
)
=
f
(
p
n
)
−
f
(
p
)
.
Furthermore, it is given that
f
(
2
2014
)
+
f
(
3
2015
)
+
f
(
5
2016
)
=
2013
f(2^{2014})+f(3^{2015})+f(5^{2016})=2013
f
(
2
2014
)
+
f
(
3
2015
)
+
f
(
5
2016
)
=
2013
. Determine
f
(
201
4
2
)
+
f
(
201
5
3
)
+
f
(
201
6
5
)
f(2014^2)+f(2015^3)+f(2016^5)
f
(
201
4
2
)
+
f
(
201
5
3
)
+
f
(
201
6
5
)
.
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