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Israel Team Selection Test
2021 Israel TST
2
Unbounded functions.
Unbounded functions.
Source: ISR 2021 February TST p.2
May 4, 2022
functional equation
functional equation in Z
algebra
Problem Statement
Find all unbounded functions
f
:
Z
→
Z
f:\mathbb Z \rightarrow \mathbb Z
f
:
Z
→
Z
, such that
f
(
f
(
x
)
−
y
)
∣
x
−
f
(
y
)
f(f(x)-y)|x-f(y)
f
(
f
(
x
)
−
y
)
∣
x
−
f
(
y
)
holds for any integers
x
,
y
x,y
x
,
y
.
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