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Problems
Contests
National and Regional Contests
PEN Problems
PEN K Problems
12
12
Part of
PEN K Problems
Problems
(1)
K 12
Source:
5/25/2007
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
: [*]
f
(
2
)
=
2
f(2)=2
f
(
2
)
=
2
, [*]
f
(
m
n
)
=
f
(
m
)
f
(
n
)
f(mn)=f(m)f(n)
f
(
mn
)
=
f
(
m
)
f
(
n
)
, [*]
f
(
n
+
1
)
>
f
(
n
)
f(n+1)>f(n)
f
(
n
+
1
)
>
f
(
n
)
.
function
induction
Functional Equations