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National and Regional Contests
Morocco Contests
Morocco National Olympiad
2005 Morocco National Olympiad
2
2
Part of
2005 Morocco National Olympiad
Problems
(1)
interesting...
Source:
3/11/2005
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
quadratics
induction
number theory unsolved
number theory