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2020 IMO Shortlist
A6
Big function eats Eyed
Big function eats Eyed
Source: 2020 A6
July 20, 2021
algebra
functional equation
IMO Shortlist
IMO Shortlist 2020
Iteration
Problem Statement
Find all functions
f
:
Z
ā
Z
f : \mathbb{Z}\rightarrow \mathbb{Z}
f
:
Z
ā
Z
satisfying
f
a
2
+
b
2
(
a
+
b
)
=
a
f
(
a
)
+
b
f
(
b
)
f^{a^{2} + b^{2}}(a+b) = af(a) +bf(b)
f
a
2
+
b
2
(
a
+
b
)
=
a
f
(
a
)
+
b
f
(
b
)
for all integers
a
a
a
and
b
b
b
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