MathDB
Problems
Contests
National and Regional Contests
PEN Problems
PEN H Problems
38
38
Part of
PEN H Problems
Problems
(1)
H 38
Source:
5/25/2007
Suppose that
p
p
p
is an odd prime such that
2
p
+
1
2p+1
2
p
+
1
is also prime. Show that the equation
x
p
+
2
y
p
+
5
z
p
=
0
x^{p}+2y^{p}+5z^{p}=0
x
p
+
2
y
p
+
5
z
p
=
0
has no solutions in integers other than
(
0
,
0
,
0
)
(0,0,0)
(
0
,
0
,
0
)
.
abstract algebra
Diophantine Equations