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Problems
Contests
National and Regional Contests
PEN Problems
PEN H Problems
3
3
Part of
PEN H Problems
Problems
(1)
H 3
Source:
5/25/2007
Does there exist a solution to the equation
x
2
+
y
2
+
z
2
+
u
2
+
v
2
=
x
y
z
u
v
ā
65
x^{2}+y^{2}+z^{2}+u^{2}+v^{2}=xyzuv-65
x
2
+
y
2
+
z
2
+
u
2
+
v
2
=
x
yz
uv
ā
65
in integers with
x
,
y
,
z
,
u
,
v
x, y, z, u, v
x
,
y
,
z
,
u
,
v
greater than
1998
1998
1998
?
quadratics
Diophantine Equations