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Austrian-Polish
2005 Austrian-Polish Competition
6
Cauchy with powers
Cauchy with powers
Source: Austrian-Polish 2005, Problem 6
July 5, 2015
functional equation
algebra
Cauchy functional equation
Sum of powers
Problem Statement
Determine all monotone functions
f
:
Z
→
Z
f: \mathbb{Z} \rightarrow \mathbb{Z}
f
:
Z
→
Z
, so that for all
x
,
y
∈
Z
x, y \in \mathbb{Z}
x
,
y
∈
Z
f
(
x
2005
+
y
2005
)
=
(
f
(
x
)
)
2005
+
(
f
(
y
)
)
2005
f(x^{2005} + y^{2005}) = (f(x))^{2005} + (f(y))^{2005}
f
(
x
2005
+
y
2005
)
=
(
f
(
x
)
)
2005
+
(
f
(
y
)
)
2005
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