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National and Regional Contests
PEN Problems
PEN H Problems
83
83
Part of
PEN H Problems
Problems
(1)
H 83
Source:
5/25/2007
Find all pairs
(
a
,
b
)
(a, b)
(
a
,
b
)
of positive integers such that
(
a
3
+
b
3
−
1
)
2
=
49
+
20
6
3
.
(\sqrt[3]{a}+\sqrt[3]{b}-1 )^{2}= 49+20 \sqrt[3]{6}.
(
3
a
+
3
b
−
1
)
2
=
49
+
20
3
6
.
Diophantine Equations