MathDB
Problems
Contests
International Contests
Baltic Way
2022 Baltic Way
16
16
Part of
2022 Baltic Way
Problems
(1)
Classical NT FE
Source: Baltic Way 2022, Problem 16
11/12/2022
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
+
number theory