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Kosovo Team Selection Test
2011 Kosovo Team Selection Test
3
Set Problem (KSV IMO TST 2011)
Set Problem (KSV IMO TST 2011)
Source:
April 25, 2011
modular arithmetic
number theory unsolved
number theory
Problem Statement
Let
n
n
n
be a natural number, for which we define
S
(
n
)
=
{
1
+
g
+
g
2
+
.
.
.
+
g
n
−
1
∣
g
∈
N
,
g
≥
2
}
S(n)=\{1+g+g^2+...+g^{n-1}|g\in{\mathbb{N}},g\geq2\}
S
(
n
)
=
{
1
+
g
+
g
2
+
...
+
g
n
−
1
∣
g
∈
N
,
g
≥
2
}
a
)
a)
a
)
Prove that:
S
(
3
)
∩
S
(
4
)
=
∅
S(3)\cap S(4)=\varnothing
S
(
3
)
∩
S
(
4
)
=
∅
b
)
b)
b
)
Determine:
S
(
3
)
∩
S
(
5
)
S(3)\cap S(5)
S
(
3
)
∩
S
(
5
)
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