MathDB
Problems
Contests
National and Regional Contests
France Contests
France Team Selection Test
2007 France Team Selection Test
2
France TST 2007
France TST 2007
Source: Problem 5
May 16, 2007
function
induction
algebra
functional equation
algebra proposed
Problem Statement
Find all functions
f
:
Z
→
Z
f: \mathbb{Z}\rightarrow\mathbb{Z}
f
:
Z
→
Z
such that for all
x
,
y
∈
Z
x,y \in \mathbb{Z}
x
,
y
∈
Z
:
f
(
x
−
y
+
f
(
y
)
)
=
f
(
x
)
+
f
(
y
)
.
f(x-y+f(y))=f(x)+f(y).
f
(
x
−
y
+
f
(
y
))
=
f
(
x
)
+
f
(
y
)
.
Back to Problems
View on AoPS