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1992 Polish MO Finals
2
functional equation in Q+
functional equation in Q+
Source: Problem 2, Polish NO 1992
October 1, 2005
function
algebra unsolved
algebra
Problem Statement
Find all functions
f
:
Q
+
ā
Q
+
f : \mathbb{Q}^{+} \rightarrow \mathbb{Q}^{+}
f
:
Q
+
ā
Q
+
, where
Q
+
\mathbb{Q}^{+}
Q
+
is the set of positive rationals, such that
f
(
x
+
1
)
=
f
(
x
)
+
1
f(x+1) = f(x) + 1
f
(
x
+
1
)
=
f
(
x
)
+
1
and
f
(
x
3
)
=
f
(
x
)
3
f(x^3) = f(x)^3
f
(
x
3
)
=
f
(
x
)
3
for all
x
x
x
.
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