MathDB
Problems
Contests
National and Regional Contests
Turkey Contests
Turkey Team Selection Test
2016 Turkey Team Selection Test
5
Functional Number Theory (Turkey IMO TST 2016 P5)
Functional Number Theory (Turkey IMO TST 2016 P5)
Source: Turkey IMO TST 2016 P5
April 5, 2016
function
number theory
functional equation
Divisibility
Problem Statement
Find all functions
f
:
N
→
N
f: \mathbb{N} \to \mathbb{N}
f
:
N
→
N
such that for all
m
,
n
∈
N
m,n \in \mathbb{N}
m
,
n
∈
N
holds
f
(
m
n
)
=
f
(
m
)
f
(
n
)
f(mn)=f(m)f(n)
f
(
mn
)
=
f
(
m
)
f
(
n
)
and
m
+
n
∣
f
(
m
)
+
f
(
n
)
m+n \mid f(m)+f(n)
m
+
n
∣
f
(
m
)
+
f
(
n
)
.
Back to Problems
View on AoPS