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2016 LMT
8
2016 LMT Theme #8
2016 LMT Theme #8
Source:
April 11, 2016
Problem Statement
Consider the function
f
:
[
0
,
1
)
→
[
0
,
1
)
f:[0,1)\rightarrow[0,1)
f
:
[
0
,
1
)
→
[
0
,
1
)
defined by
f
(
x
)
=
2
x
−
⌊
2
x
⌋
f(x)=2x-\lfloor 2x\rfloor
f
(
x
)
=
2
x
−
⌊
2
x
⌋
, where
⌊
2
x
⌋
\lfloor 2x\rfloor
⌊
2
x
⌋
is the greatest integer less than or equal to
2
x
2x
2
x
. Find the sum of all values of
x
x
x
such that
f
17
(
x
)
=
x
.
f^{17}(x)=x.
f
17
(
x
)
=
x
.
Proposed by Matthew Weiss
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