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National and Regional Contests
Iran Contests
Iran MO (3rd Round)
2023 Iran MO (3rd Round)
4
4
Part of
2023 Iran MO (3rd Round)
Problems
(1)
Another easy FE
Source: Iran MO 3rd round 2023 ,Day 2 P1
8/16/2023
For any function
f
:
N
→
N
f:\mathbb{N}\to\mathbb{N}
f
:
N
→
N
we define
P
(
n
)
=
f
(
1
)
f
(
2
)
.
.
.
f
(
n
)
P(n)=f(1)f(2)...f(n)
P
(
n
)
=
f
(
1
)
f
(
2
)
...
f
(
n
)
. Find all functions
f
:
N
→
N
f:\mathbb{N}\to\mathbb{N}
f
:
N
→
N
st for each
a
,
b
a,b
a
,
b
:
P
(
a
)
+
P
(
b
)
∣
a
!
+
b
!
P(a)+P(b) | a! + b!
P
(
a
)
+
P
(
b
)
∣
a
!
+
b
!
algebra