MathDB
Problems
Contests
National and Regional Contests
Greece Contests
Greece JBMO TST
2001 Greece JBMO TST
1
1
Part of
2001 Greece JBMO TST
Problems
(1)
factorization and x^4+y^4+z^4-2x^2y^2-2y^2z^2-2z^2x^2=2000 in ZxZxZ
Source: Greece JBMO TST 2001 p1
6/17/2019
a) Factorize
A
=
x
4
+
y
4
+
z
4
−
2
x
2
y
2
−
2
y
2
z
2
−
2
z
2
x
2
A= x^4+y^4+z^4-2x^2y^2-2y^2z^2-2z^2x^2
A
=
x
4
+
y
4
+
z
4
−
2
x
2
y
2
−
2
y
2
z
2
−
2
z
2
x
2
b) 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
number theory
algebra
factorization
Diophantine equation