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2004 Argentina National Olympiad
2
a^2c =b^2d , ab+cd =2^{99}+2^{101}
a^2c =b^2d , ab+cd =2^{99}+2^{101}
Source: Argentina 2004 OMA L3 p2
May 12, 2024
number theory
system of equations
Diophantine Equations
Problem Statement
Determine all positive integers
a
,
b
,
c
,
d
a,b,c,d
a
,
b
,
c
,
d
such that
{
a
<
b
a
2
c
=
b
2
d
a
b
+
c
d
=
2
99
+
2
101
\begin{cases} a<b \\ a^2c =b^2d \\ ab+cd =2^{99}+2^{101} \end{cases}
⎩
⎨
⎧
a
<
b
a
2
c
=
b
2
d
ab
+
c
d
=
2
99
+
2
101
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