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Saint Petersburg Mathematical Olympiad
2010 Saint Petersburg Mathematical Olympiad
1
System of equations
System of equations
Source: St Petersburg Olympiad 2010, Grade 11, P1
September 14, 2017
algebra
system of equations
Problem Statement
Solve in positives
x
y
=
z
,
y
z
=
x
,
z
x
=
y
x^y=z,y^z=x,z^x=y
x
y
=
z
,
y
z
=
x
,
z
x
=
y
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