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Problems
Contests
National and Regional Contests
PEN Problems
PEN H Problems
89
89
Part of
PEN H Problems
Problems
(1)
H 89
Source:
5/25/2007
Prove that the number
99999
+
111111
3
99999+111111\sqrt{3}
99999
+
111111
3
cannot be written in the form
(
A
+
B
3
)
2
(A+B\sqrt{3})^2
(
A
+
B
3
)
2
, where
A
A
A
and
B
B
B
are integers.
Diophantine Equations