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VTRMC
2005 VTRMC
Problem 2
Problem 2
Part of
2005 VTRMC
Problems
(1)
k+σ(k)=2^n, permutation of [20]
Source: VTRMC 2005 P2
6/10/2021
Find, and write out explicitly, a permutation
{
p
(
1
)
,
p
(
2
)
,
…
,
p
(
20
)
}
\{p(1),p(2),\ldots,p(20)\}
{
p
(
1
)
,
p
(
2
)
,
…
,
p
(
20
)}
of
{
1
,
2
,
…
,
20
}
\{1,2,\ldots,20\}
{
1
,
2
,
…
,
20
}
such that
k
+
p
(
k
)
k+p(k)
k
+
p
(
k
)
is a power of
2
2
2
for
k
=
1
,
2
,
…
,
20
k=1,2,\ldots,20
k
=
1
,
2
,
…
,
20
, and prove that only one such permutation exists.
number theory