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Saint Petersburg Mathematical Olympiad
2009 Saint Petersburg Mathematical Olympiad
1
Division
Division
Source: St Petersburg Olympiad 2009, Grade 9, P1
August 30, 2017
number theory
Problem Statement
b
,
c
b,c
b
,
c
are naturals.
b
∣
c
+
1
b|c+1
b
∣
c
+
1
Prove that exists such natural
x
,
y
,
z
x,y,z
x
,
y
,
z
that
x
+
y
=
b
z
,
x
y
=
c
z
x+y=bz,xy=cz
x
+
y
=
b
z
,
x
y
=
cz
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