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Korea National Olympiad
1996 Korea National Olympiad
2
2
Part of
1996 Korea National Olympiad
Problems
(1)
FE integers
Source: 1996 Korea National Math olympiad #2
3/22/2018
Let the
f
:
N
→
N
f:\mathbb{N}\rightarrow\mathbb{N}
f
:
N
→
N
be the function such that (i) For all positive integers
n
,
n,
n
,
f
(
n
+
f
(
n
)
)
=
f
(
n
)
f(n+f(n))=f(n)
f
(
n
+
f
(
n
))
=
f
(
n
)
(ii)
f
(
n
o
)
=
1
f(n_o)=1
f
(
n
o
)
=
1
for some
n
0
n_0
n
0
Prove that
f
(
n
)
≡
1.
f(n)\equiv 1.
f
(
n
)
≡
1.
functional equation
algebra
number theory
function