MathDB
Problems
Contests
National and Regional Contests
PEN Problems
PEN K Problems
25
25
Part of
PEN K Problems
Problems
(1)
K 25
Source:
5/25/2007
Consider all functions
f
:
N
ā
N
f:\mathbb{N}\to\mathbb{N}
f
:
N
ā
N
satisfying
f
(
t
2
f
(
s
)
)
=
s
(
f
(
t
)
)
2
f(t^2 f(s)) = s(f(t))^2
f
(
t
2
f
(
s
))
=
s
(
f
(
t
)
)
2
for all
s
s
s
and
t
t
t
in
N
N
N
. Determine the least possible value of
f
(
1998
)
f(1998)
f
(
1998
)
.
function
induction
Functional Equations