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1997 South africa National Olympiad
4
Functional equation with integers
Functional equation with integers
Source: South Africa 1997
October 8, 2005
function
algebra
functional equation
algebra unsolved
Problem Statement
Find all functions
f
:
Z
→
Z
f: \mathbb{Z} \rightarrow \mathbb{Z}
f
:
Z
→
Z
which satisfy
f
(
m
+
f
(
n
)
)
=
f
(
m
)
+
n
f(m + f(n)) = f(m) + n
f
(
m
+
f
(
n
))
=
f
(
m
)
+
n
for all
m
,
n
∈
Z
m,n \in \mathbb{Z}
m
,
n
∈
Z
.
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