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2018 Pan African
1
All functions f over Z such that (f(x + y))^2 = f(x^2) + f(y^2) [PAMO 2018]
All functions f over Z such that (f(x + y))^2 = f(x^2) + f(y^2) [PAMO 2018]
Source: Pan African Math Olympiad 2018, Problem 1
June 30, 2018
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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