MathDB
Problems
Contests
National and Regional Contests
Argentina Contests
Argentina National Olympiad
2004 Argentina National Olympiad
2
2
Part of
2004 Argentina National Olympiad
Problems
(1)
a^2c =b^2d , ab+cd =2^{99}+2^{101}
Source: Argentina 2004 OMA L3 p2
5/12/2024
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
number theory
system of equations
Diophantine Equations