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Malaysia National Olympiad
2019 Malaysia National Olympiad
4
4
Part of
2019 Malaysia National Olympiad
Problems
(1)
Counting subset sizes
Source: Malaysia National Math Olympiad - Sulong Problem 4
10/26/2019
Let
A
=
{
1
,
2
,
.
.
.
,
100
}
A=\{1,2,...,100\}
A
=
{
1
,
2
,
...
,
100
}
and
f
(
k
)
,
k
ā
N
f(k), k\in N
f
(
k
)
,
k
ā
N
be the size of the largest subset of
A
A
A
such that no two elements differ by
k
k
k
. How many solutions are there to
f
(
k
)
=
50
f(k)=50
f
(
k
)
=
50
?
number theory