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2023 HMIC
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P1
Part of
2023 HMIC
Problems
(1)
functional equations over positive rationals make me big sad
Source: 2023 HMIC P1
4/25/2023
Let
Q
+
\mathbb{Q}^{+}
Q
+
denote the set of positive rational numbers. Find, with proof, all functions
f
:
Q
+
ā
Q
+
f:\mathbb{Q}^+ \to \mathbb{Q}^+
f
:
Q
+
ā
Q
+
such that, for all positive rational numbers
x
x
x
and
y
,
y,
y
,
we have
f
(
x
)
=
f
(
x
+
y
)
+
f
(
x
+
x
2
f
(
y
)
)
.
f(x)=f(x+y)+f(x+x^2f(y)).
f
(
x
)
=
f
(
x
+
y
)
+
f
(
x
+
x
2
f
(
y
))
.
algebra
functional equation
HMIC