MathDB
Problems
Contests
International Contests
IMO Shortlist
2015 IMO Shortlist
A2
integer functional equation
integer functional equation
Source: 2015 IMO Shortlist A2
July 7, 2016
IMO Shortlist
functional equation
Problem Statement
Determine all functions
f
:
Z
→
Z
f:\mathbb{Z}\rightarrow\mathbb{Z}
f
:
Z
→
Z
with the property that
f
(
x
−
f
(
y
)
)
=
f
(
f
(
x
)
)
−
f
(
y
)
−
1
f(x-f(y))=f(f(x))-f(y)-1
f
(
x
−
f
(
y
))
=
f
(
f
(
x
))
−
f
(
y
)
−
1
holds for all
x
,
y
∈
Z
x,y\in\mathbb{Z}
x
,
y
∈
Z
.
Back to Problems
View on AoPS