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No integers satisfying the equation - JBMO Shortlist
No integers satisfying the equation - JBMO Shortlist
Source:
October 30, 2010
modular arithmetic
number theory
number theory proposed
Problem Statement
Prove that there are no integers
x
,
y
,
z
x,y,z
x
,
y
,
z
such that
x
4
+
y
4
+
z
4
−
2
x
2
y
2
−
2
y
2
z
2
−
2
z
2
x
2
=
2000
x^4+y^4+z^4-2x^2y^2-2y^2z^2-2z^2x^2=2000
x
4
+
y
4
+
z
4
−
2
x
2
y
2
−
2
y
2
z
2
−
2
z
2
x
2
=
2000
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