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Thailand Contests
Thailand TST Selection Test
2017 Thailand TSTST
2
sum i of (sum j of (f(i)-g(j))^(2559))
sum i of (sum j of (f(i)-g(j))^(2559))
Source: 2016 Thailand October Camp 2.2
February 26, 2022
bijection
function
algebra
Problem Statement
Let
f
,
g
f, g
f
,
g
be bijections on
{
1
,
2
,
3
,
…
,
2016
}
\{1, 2, 3, \dots, 2016\}
{
1
,
2
,
3
,
…
,
2016
}
. Determine the value of
∑
i
=
1
2016
∑
j
=
1
2016
[
f
(
i
)
−
g
(
j
)
]
2559
.
\sum_{i=1}^{2016}\sum_{j=1}^{2016}[f(i)-g(j)]^{2559}.
i
=
1
∑
2016
j
=
1
∑
2016
[
f
(
i
)
−
g
(
j
)
]
2559
.
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