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Saint Petersburg Mathematical Olympiad
2012 Saint Petersburg Mathematical Olympiad
2
Find minimal
Find minimal
Source: St Petersburg Olympiad 2012, Grade 9, P2
September 29, 2017
number theory
Problem Statement
Natural
a
,
b
,
c
a,b,c
a
,
b
,
c
are
>
100
>100
>
100
and
(
a
,
b
,
c
)
=
1
(a,b,c)=1
(
a
,
b
,
c
)
=
1
.
c
∣
a
+
b
,
a
∣
b
+
c
c|a+b,a|b+c
c
∣
a
+
b
,
a
∣
b
+
c
Find minimal
b
b
b
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