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Rational solutions a^2 + c^2 + 17(b^2 + d^2)=21, ab + cd = 2
Rational solutions a^2 + c^2 + 17(b^2 + d^2)=21, ab + cd = 2
Source:
September 1, 2010
algebra
system of equations
Diophantine Equations
polynomial
IMO Shortlist
IMO Longlist
Problem Statement
Find all rational solutions of
a
2
+
c
2
+
17
(
b
2
+
d
2
)
=
21
,
a^2 + c^2 + 17(b^2 + d^2) = 21,
a
2
+
c
2
+
17
(
b
2
+
d
2
)
=
21
,
a
b
+
c
d
=
2.
ab + cd = 2.
ab
+
c
d
=
2.
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