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2017-IMOC
N5
N5
Part of
2017-IMOC
Problems
(1)
f(x)+f(y)|x^2-y^2 over N
Source: IMOC 2017 N5
8/14/2021
Find all functions
f
:
N
→
N
f:\mathbb N\to\mathbb N
f
:
N
→
N
such that
f
(
x
)
+
f
(
y
)
∣
x
2
−
y
2
f(x)+f(y)\mid x^2-y^2
f
(
x
)
+
f
(
y
)
∣
x
2
−
y
2
holds for all
x
,
y
∈
N
x,y\in\mathbb N
x
,
y
∈
N
.
number theory
fe
functional equation