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2021 APMO
5
Perfect Square Function
Perfect Square Function
Source: 2021 APMO P5
June 9, 2021
function
number theory
functional equation
APMO
Problem Statement
Determine all Functions
f
:
Z
→
Z
f:\mathbb{Z} \to \mathbb{Z}
f
:
Z
→
Z
such that
f
(
f
(
a
)
−
b
)
+
b
f
(
2
a
)
f(f(a)-b)+bf(2a)
f
(
f
(
a
)
−
b
)
+
b
f
(
2
a
)
is a perfect square for all integers
a
a
a
and
b
b
b
.
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