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2000 South africa National Olympiad
5
Functional equation with integers
Functional equation with integers
Source: South Africa 2000
September 30, 2005
function
algebra unsolved
algebra
Problem Statement
Find all functions
f
:
Z
→
Z
f: \mathbb{Z} \rightarrow \mathbb{Z}
f
:
Z
→
Z
(where
Z
\mathbb{Z}
Z
is the set of all integers) such that
2000
f
(
f
(
x
)
)
−
3999
f
(
x
)
+
1999
x
=
0
for all
x
∈
Z
.
2000f(f(x)) - 3999f(x) + 1999x = 0\textrm{ for all }x \in \mathbb{Z}.
2000
f
(
f
(
x
))
−
3999
f
(
x
)
+
1999
x
=
0
for all
x
∈
Z
.
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