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2022 Iberoamerican
6
f(a)f(a+b)-ab is a square
f(a)f(a+b)-ab is a square
Source: Iberoamerican 2022, Day 2, P3
September 29, 2022
number theory
functional equation
Problem Statement
Find all functions
f
:
N
→
N
f:\mathbb{N} \rightarrow \mathbb{N}
f
:
N
→
N
, such that
f
(
a
)
f
(
a
+
b
)
−
a
b
f(a)f(a+b)-ab
f
(
a
)
f
(
a
+
b
)
−
ab
is a perfect square for all
a
,
b
∈
N
a, b \in \mathbb{N}
a
,
b
∈
N
.
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