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Soros Olympiad in Mathematics
III Soros Olympiad 1996 - 97 (Russia)
10.4
2x2 diophantine: ab+cd=34, ac-bd=19 (III Soros Olympiad 1996-97 R3 10.4)
2x2 diophantine: ab+cd=34, ac-bd=19 (III Soros Olympiad 1996-97 R3 10.4)
Source:
May 31, 2024
number theory
system of equations
Problem Statement
Find natural
a
,
b
,
c
,
d
a, b, c, d
a
,
b
,
c
,
d
that satisfy the system
{
a
b
+
c
d
=
34
a
c
−
b
d
=
19
\begin{cases} ab+cd=34 \\ ac-bd=19 \end{cases}
{
ab
+
c
d
=
34
a
c
−
b
d
=
19
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