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2002 Czech-Polish-Slovak Match
3
How many functions satisfy f^(4)(x)+x=n+1?
How many functions satisfy f^(4)(x)+x=n+1?
Source: Czech-Polish-Slovak 2002 Q3
April 28, 2013
function
algebra unsolved
algebra
Problem Statement
Let
S
=
{
1
,
2
,
⋯
,
n
}
,
n
∈
N
S = \{1, 2, \cdots , n\}, n \in N
S
=
{
1
,
2
,
⋯
,
n
}
,
n
∈
N
. Find the number of functions
f
:
S
→
S
f : S \to S
f
:
S
→
S
with the property that
x
+
f
(
f
(
f
(
f
(
x
)
)
)
)
=
n
+
1
x + f(f(f(f(x)))) = n + 1
x
+
f
(
f
(
f
(
f
(
x
))))
=
n
+
1
for all
x
∈
S
x \in S
x
∈
S
?
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