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Problems
Contests
National and Regional Contests
PEN Problems
PEN K Problems
26
26
Part of
PEN K Problems
Problems
(1)
K 26
Source:
5/25/2007
The function
f
:
N
→
N
0
f: \mathbb{N}\to\mathbb{N}_{0}
f
:
N
→
N
0
satisfies for all
m
,
n
∈
N
m,n\in\mathbb{N}
m
,
n
∈
N
:
f
(
m
+
n
)
−
f
(
m
)
−
f
(
n
)
=
0
or
1
,
f
(
2
)
=
0
,
f
(
3
)
>
0
,
and
f
(
9999
)
=
3333.
f(m+n)-f(m)-f(n)=0\text{ or }1, \; f(2)=0, \; f(3)>0, \; \text{ and }f(9999)=3333.
f
(
m
+
n
)
−
f
(
m
)
−
f
(
n
)
=
0
or
1
,
f
(
2
)
=
0
,
f
(
3
)
>
0
,
and
f
(
9999
)
=
3333.
Determine
f
(
1982
)
f(1982)
f
(
1982
)
.
function
calculus
integration
induction
Functional Equations