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Baltic Way
2022 Baltic Way
16
Classical NT FE
Classical NT FE
Source: Baltic Way 2022, Problem 16
November 12, 2022
number theory
Problem Statement
Let
Z
+
\mathbb{Z^+}
Z
+
denote the set of positive integers. Find all functions
f
:
Z
+
→
Z
+
f:\mathbb{Z^+} \to \mathbb{Z^+}
f
:
Z
+
→
Z
+
satisfying the condition
f
(
a
)
+
f
(
b
)
∣
(
a
+
b
)
2
f(a) + f(b) \mid (a + b)^2
f
(
a
)
+
f
(
b
)
∣
(
a
+
b
)
2
for all
a
,
b
∈
Z
+
a,b \in \mathbb{Z^+}
a
,
b
∈
Z
+
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