MathDB
Problems
Contests
National and Regional Contests
Malaysia Contests
Malaysian IMO Training Camp
BIMO 2022
5
5
Part of
BIMO 2022
Problems
(1)
rad(f(a)f(b)+f(b)f(c)+f(c)f(a))=rad(ab+bc+ca)
Source: Malaysian IMO TST 2022 P5
5/13/2022
Find all functions
f
:
Z
→
Z
f : \mathbb{Z}\rightarrow \mathbb{Z}
f
:
Z
→
Z
such that for all prime
p
p
p
the following condition holds:
p
∣
a
b
+
b
c
+
c
a
⟺
p
∣
f
(
a
)
f
(
b
)
+
f
(
b
)
f
(
c
)
+
f
(
c
)
f
(
a
)
p \mid ab + bc + ca \iff p \mid f(a)f(b) + f(b)f(c) + f(c)f(a)
p
∣
ab
+
b
c
+
c
a
⟺
p
∣
f
(
a
)
f
(
b
)
+
f
(
b
)
f
(
c
)
+
f
(
c
)
f
(
a
)
Proposed by Anzo Teh Zhao Yang
number theory