MathDB
Problems
Contests
National and Regional Contests
Taiwan Contests
IMOC Shortlist
2018-IMOC
N1
N1
Part of
2018-IMOC
Problems
(1)
iterated divisibility FE
Source: IMOC 2018 N1
8/17/2021
Find all functions
f
:
N
→
N
f:\mathbb N\to\mathbb N
f
:
N
→
N
satisfying
x
+
f
f
(
x
)
(
y
)
∣
2
(
x
+
y
)
x+f^{f(x)}(y)\mid2(x+y)
x
+
f
f
(
x
)
(
y
)
∣
2
(
x
+
y
)
for all
x
,
y
∈
N
x,y\in\mathbb N
x
,
y
∈
N
.
fe
functional equation
number theory