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2004 Romania National Olympiad
2
Diophantic
Diophantic
Source: RMO 2004, Grade 8, Problem 2
February 26, 2006
modular arithmetic
inequalities
Problem Statement
Prove that the equation
x
2
+
y
2
+
z
2
+
t
2
=
2
2004
x^2+y^2+z^2+t^2=2^{2004}
x
2
+
y
2
+
z
2
+
t
2
=
2
2004
, where
0
≤
x
≤
y
≤
z
≤
t
0 \leq x \leq y \leq z \leq t
0
≤
x
≤
y
≤
z
≤
t
, has exactly
2
2
2
solutions in
Z
\mathbb Z
Z
. Mihai Baluna
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