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2018 Pan-African Shortlist
A1
PAMO Problem 1: Functional Equation
PAMO Problem 1: Functional Equation
Source: 2018 Pan-African Mathematics Olympiad
July 3, 2018
functional equation
algebra
function
Problem Statement
Find all functions
f
:
Z
→
Z
f : \mathbb{Z} \to \mathbb{Z}
f
:
Z
→
Z
such that
(
f
(
x
+
y
)
)
2
=
f
(
x
2
)
+
f
(
y
2
)
(f(x + y))^2 = f(x^2) + f(y^2)
(
f
(
x
+
y
)
)
2
=
f
(
x
2
)
+
f
(
y
2
)
for all
x
,
y
∈
Z
x, y \in \mathbb{Z}
x
,
y
∈
Z
.
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