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Contests
National and Regional Contests
Czech Republic Contests
Czech and Slovak Olympiad III A
2007 Czech and Slovak Olympiad III A
3
3
Part of
2007 Czech and Slovak Olympiad III A
Problems
(1)
the smallest possible value for f(2007)
Source: Czech and Slovak third round,2007,p3
3/3/2012
Consider a function
f
:
N
ā
N
f:\mathbb N\rightarrow \mathbb N
f
:
N
ā
N
such that for any two positive integers
x
,
y
x,y
x
,
y
, the equation
f
(
x
f
(
y
)
)
=
y
f
(
x
)
f(xf(y))=yf(x)
f
(
x
f
(
y
))
=
y
f
(
x
)
holds. Find the smallest possible value of
f
(
2007
)
f(2007)
f
(
2007
)
.
function
algebra
functional equation
algebra unsolved