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Mediterranean Mathematics Olympiad
2003 Mediterranean Mathematics Olympiad
1
Prove that the equation has no rational solutions
Prove that the equation has no rational solutions
Source: Mediterranean MO 2003
October 31, 2010
algebra proposed
algebra
Problem Statement
Prove that the equation
x
2
+
y
2
+
z
2
=
x
+
y
+
z
+
1
x^2 + y^2 + z^2 = x + y + z + 1
x
2
+
y
2
+
z
2
=
x
+
y
+
z
+
1
has no rational solutions.
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