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7
2000 Advanced Topics #7: Equations in Positive Integers
2000 Advanced Topics #7: Equations in Positive Integers
Source:
June 21, 2012
Problem Statement
Assume that
a
,
b
,
c
,
d
a,b,c,d
a
,
b
,
c
,
d
are positive integers, and
a
c
=
b
d
=
3
4
\dfrac{a}{c}=\dfrac{b}{d}=\dfrac{3}{4}
c
a
=
d
b
=
4
3
,
a
2
+
c
2
−
b
2
+
d
2
=
15
\sqrt{a^2+c^2}-\sqrt{b^2+d^2}=15
a
2
+
c
2
−
b
2
+
d
2
=
15
. Find
a
c
+
b
d
−
a
d
−
b
c
ac+bd-ad-bc
a
c
+
b
d
−
a
d
−
b
c
.
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