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National and Regional Contests
Iran Contests
Iran Team Selection Test
2005 Iran Team Selection Test
1
f:N -->N
f:N -->N
Source: Iran TST 2005
April 20, 2005
function
number theory proposed
number theory
Problem Statement
Find all
f
:
N
⟼
N
f : N \longmapsto N
f
:
N
⟼
N
that there exist
k
∈
N
k \in N
k
∈
N
and a prime
p
p
p
that:
∀
n
≥
k
f
(
n
+
p
)
=
f
(
n
)
\forall n \geq k \ f(n+p)=f(n)
∀
n
≥
k
f
(
n
+
p
)
=
f
(
n
)
and also if
m
∣
n
m \mid n
m
∣
n
then
f
(
m
+
1
)
∣
f
(
n
)
+
1
f(m+1) \mid f(n)+1
f
(
m
+
1
)
∣
f
(
n
)
+
1
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