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Pan African
2024 Pan-African
5
5
Part of
2024 Pan-African
Problems
(1)
Functional equations
Source: Pan African Mathematics Olympiad p5
8/16/2024
Let
R
\mathbb{R}
R
denote the set of real numbers. Find all functions
f
:
R
→
R
f: \mathbb{R} \to \mathbb{R}
f
:
R
→
R
such that
f
(
x
2
)
−
y
f
(
y
)
=
f
(
x
+
y
)
(
f
(
x
)
−
y
)
f(x^2) - y f(y) = f(x+y)(f(x) - y)
f
(
x
2
)
−
y
f
(
y
)
=
f
(
x
+
y
)
(
f
(
x
)
−
y
)
for all real numbers
x
x
x
and
y
y
y
.
algebra
functional equation
PAMO 2024