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Miklós Schweitzer
1971 Miklós Schweitzer
3
3
Part of
1971 Miklós Schweitzer
Problems
(1)
Miklos Schweitzer 1971_3
Source:
10/29/2008
Let
0
<
a
k
<
1
0<a_k<1
0
<
a
k
<
1
for
k
=
1
,
2
,
.
.
.
.
k=1,2,... .
k
=
1
,
2
,
....
Give a necessary and sufficient condition for the existence, for every
0
<
x
<
1
0<x<1
0
<
x
<
1
, of a permutation
π
x
\pi_x
π
x
of the positive integers such that
x
=
∑
k
=
1
∞
a
π
x
(
k
)
2
k
.
x= \sum_{k=1}^{\infty} \frac{a_{\pi_x}(k)}{2^k}.
x
=
k
=
1
∑
∞
2
k
a
π
x
(
k
)
.
P. Erdos
real analysis