MathDB
Problems
Contests
National and Regional Contests
Netherlands Contests
Dutch BxMO/EGMO TST
2017 Dutch BxMO TST
2
2
Part of
2017 Dutch BxMO TST
Problems
(1)
beautiful functional equation problem
Source: Netherlands TST for BxMO 2017 problem 2
2/1/2018
Let define a function
f
:
N
→
Z
f: \mathbb{N} \rightarrow \mathbb{Z}
f
:
N
→
Z
such that :
i
)
i)
i
)
f
(
p
)
=
1
f(p)=1
f
(
p
)
=
1
for all prime numbers
p
p
p
.
i
i
)
ii)
ii
)
f
(
x
y
)
=
x
f
(
y
)
+
y
f
(
x
)
f(xy)=xf(y)+yf(x)
f
(
x
y
)
=
x
f
(
y
)
+
y
f
(
x
)
for all positive integers
x
,
y
x,y
x
,
y
find the smallest
n
≥
2016
n \geq 2016
n
≥
2016
such that
f
(
n
)
=
n
f(n)=n
f
(
n
)
=
n
function
number theory
prime numbers