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National and Regional Contests
PEN Problems
PEN H Problems
14
14
Part of
PEN H Problems
Problems
(1)
H 14
Source:
5/25/2007
Show that the equation
x
2
+
y
5
=
z
3
x^2 +y^5 =z^3
x
2
+
y
5
=
z
3
has infinitely many solutions in integers
x
,
y
,
z
x, y, z
x
,
y
,
z
for which
x
y
z
≠
0
xyz \neq 0
x
yz
=
0
.
Diophantine Equations
pen