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2005 Morocco National Olympiad
2
interesting...
interesting...
Source:
March 11, 2005
quadratics
induction
number theory unsolved
number theory
Problem Statement
Find all the positive integers
x
,
y
,
z
x,y,z
x
,
y
,
z
satisfiing :
x
2
+
y
2
+
z
2
=
2
x
y
z
x^{2}+y^{2}+z^{2}=2xyz
x
2
+
y
2
+
z
2
=
2
x
yz
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