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CIIM
2012 CIIM
Problem 2
CIIM 2012 Problem 2
CIIM 2012 Problem 2
Source:
June 9, 2016
CIIM
CIIM 2012
undergraduate
Problem Statement
A set
A
⊂
Z
A\subset \mathbb{Z}
A
⊂
Z
is "padre" if whenever
x
,
y
∈
A
x,y \in A
x
,
y
∈
A
with
x
≤
y
x\leq y
x
≤
y
then also
2
y
−
x
∈
A
2y -x \in A
2
y
−
x
∈
A
. Prove that if
A
A
A
is "padre",
0
,
a
,
b
∈
A
0,a,b \in A
0
,
a
,
b
∈
A
with
0
<
a
<
b
0< a < b
0
<
a
<
b
and
d
=
g
.
c
.
d
(
a
,
b
)
d = g.c.d(a,b)
d
=
g
.
c
.
d
(
a
,
b
)
then
a
+
b
−
3
d
,
a
+
b
−
2
d
∈
A
.
a+b-3d, a+b-2d \in A.
a
+
b
−
3
d
,
a
+
b
−
2
d
∈
A
.
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