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National and Regional Contests
PEN Problems
PEN H Problems
80
80
Part of
PEN H Problems
Problems
(1)
H 80
Source:
5/25/2007
Prove that if
a
,
b
,
c
,
d
a, b, c, d
a
,
b
,
c
,
d
are integers such that
d
=
(
a
+
2
3
b
+
4
3
c
)
2
d=( a+\sqrt[3]{2}b+\sqrt[3]{4}c)^{2}
d
=
(
a
+
3
2
b
+
3
4
c
)
2
then
d
d
d
is a perfect square.
Diophantine Equations